In this paper, I will prove the Riemann Hypothesis, widely considered to be the greatest unsolved mathematical problem and one of the 7 “Millennium Problems,” without. Sep 26, 2018 · “The Riemann hypothesis has been proved, unless you’re the type of person who doesn’t believe in proof by contradiction,” he said during his talk. Video created by 卫斯连大学 for the course "Introduction to Complex Analysis". of the Riemann zeta function under the truth ofthe Riemann hypothesis. Indeed, the zeroes of log (1 - x) + 2x are at 0 and somewhere above 0. Translate PDF. The hypothesis was first put forth by German mathematician Bernhard Riemann in 1859. Enoch are entirely implausible. To prove Riemann hypothesis from the functional equation concept of delta function is introduced similar to gamma and pi function. In other . of the Riemann zeta function under the truth ofthe Riemann hypothesis. THE RIEMANN HYPOTHESIS LouisdeBranges* Abstract. To prove Riemann hypothesis from the functional equation concept of delta function is introduced similar to gamma and pi function. The Riemann hypothesis is one of today's most important problems in mathematics. If f is monotone on that interval, then it's integrable. Jun 14, 2021 · This paper utilised the symmetry properties of the Riemann zeta function ζ (s) within the critical strip and its novel expression by Jeffrey et al to provide direct proof to the hypothesis. Proof of the Riemann hypothesis is number 8 of Hilbert's problems and number 1 of Smale's problems. The hypothesis states that all of the nontrivial zeros of the Riemann zeta function are located on the critical line. Mathematicians have previously shown that the Riemann hypothesis is true if all the Jensen polynomials associated with the Riemann zeta function . What is the hardest math problem?. Sep 05, 2022 · Hatem Fayed. The Riemann hypothesis, one of the last great unsolved problems in math, was first proposed in 1859 by German mathematician Bernhard Riemann. 4 thg 4, 2017. | Find, read and cite all the research you need. In this article, it is proved that the non-trivial zeros of the Riemann zeta function must lie on the critical line, known as the Riemann hypothesis. | Find, read and cite all the research you need. The Author in his works [15, 16] has shown that the Meromorphic functions that are equivalent to the Riemann zeta function are given as:. That is what will be interesting about the proof. The Riemann zeta function, defined in the graphic above, takes as its input a complex number s and adds up the . The editors refused to s. Sep 24, 2018 · Veisdal added that he would need to examine the written proof more closely to make a definitive judgement. A $1,000,000 prize has been offered by the Clay Mathematics Institute for the first correct proof of the hypothesis. Researchers would need to come up with an even more advanced proof to show the criterion is true in all cases, thereby proving the Riemann hypothesis. Analytically continuing gamma and zeta function to an extended domain, poles and. The function $ \xi(s) $ is introduced by Riemann, which zeros are identical equal to. Riemann hypothesis stands proved in three different ways. Our innovative products and services for learners, authors and customers are based on world-class research and are relevant, exciting and inspiring. Download Free PDF. Given that evidence, most mathematicians think the Riemann hypothesis is true. This hypothesis had many application in analysis and number theory. The Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers. In this article, it is proved that the non-trivial zeros of the Riemann zeta function must lie on the critical line, known as the Riemann hypothesis. Riemann hypothesis stands proved in three different ways. We prove . Your claim would suggest that 99% of mathematics is advanced math, which is a crazy scale. Before we begin, you should know that I'm not actually going to present a proof of the Riemann Hypothesis. Firstly, the limit condition of Riemann zeta-function at zeros is obtained by L’ Hospital Rule. The Riemann hypothesis is a 150-year-old puzzle that is considered by the community to be the holy grail of mathematics. 1 We create the infinite number of infinite series from the following (1) that. It has therefore been assumed for at least 150 years that the Dirichlet series representation of the zeta function is useless for characterization of the non-trivial roots. Major progress towards proving the Riemann hypothesis was made by Jacques Hadamard in 1893 [ 2 ], when he showed that the Riemann zeta function ζ ( s) can be expressed as an infinite product. Answer (1 of 11): Everything about this reeks of it being fake. A proof of the Riemann hypothesis is to be obtained for the zeta functions constructed from a discrete vector space of finite dimension over the skew-field of quaternions with rational numbers as coordinates in hyperbolic analysis on locally compact Abelian groups obtained by completion. It has therefore been assumed for at least 150 years that the Dirichlet series representation of the zeta function is useless for characterization of the non-trivial roots. Millennium Problems. 28 thg 9, 2018. Using a similar approach, we also verify that the Generalized Riemann Hypothesis is established. It predicts that the only important, or nontrivial, . com December 14, 2020 Subject Classification code- 11M26 Keywords:- Riemann Zeta function; Analytic Continuation; Critical strip; Critical line. Robin [19, Théorème 1] improved Ramanujan’s result by showing the following equivalence. Thus, we conclude that the Riemann Hypothesis is true. This checked version was submitted to a payable. The first proof of the prime number theorem used this conjecture. The hypothesis,. Kumar Eswaran, on several computer science problems especially in the neural network field. Jun 14, 2021 · This paper utilised the symmetry properties of the Riemann zeta function ζ (s) within the critical strip and its novel expression by Jeffrey et al to provide direct proof to the hypothesis. | Find, read and cite all the research you need. Analytically continuing gamma and zeta function to an extended domain, poles and. ashkiller14 • 19 hr. 00000000000 for a complex numbers. This is a carefully checked version of my 2020 proof of the Riemann Hypothesis entitled On the zeros of the Riemann zeta function, new proof. Riemann hypothesis stands proved in three different ways. of the Riemann zeta function under the truth ofthe Riemann hypothesis. This is a reformulation and refutation of a proposed proof of the Riemann hypothesis published in electronic form on the Internet in 2013 and updated in 2014. A precise version of Koch's result, due to Schoenfeld (1976), says that the Riemann hypothesis implies where is the prime-counting function, is the logarithmic integral function, and is the natural logarithm of x. Your claim would suggest that 99% of mathematics is advanced math, which is a crazy scale. We see that if the support of φ is contained in [λ − 1, λ], then the sum of the. A new proof of the Riemann Hypothesis. Riemann's Conjecture, a "One Page Proof (new)". Analytically continuing gamma and zeta function to an extended domain, poles and. This checked version was submitted to a payable. Cite as: arXiv:2209. In this paper, I will prove the Riemann Hypothesis without violating any mathematical rules or laws. . Atiyah's proof is a very good example of what a proof isn't: it doesn't contain enough detail to convince someone of the truth of his argument, . In a letter to Andrew Odlyzko, dated January 3, 1982, George Pólya said that while he was in Göttingen around 1912 to 1914 he was asked by Edmund Landau for a physical reason that the Riemann hypothesis should be true, and suggested that this would be the case if the imaginary parts t of the zeros. It has been proven that there an infinite number of non-trivial zeros. Monotone means. Answer (1 of 5): Below are four ways you can tell if a bounded function f on an interval [a,b] is Riemann integrable besides using the definition. Nov 06, 2022 · PDF | This is a straightforward approach to study the Riemann hypothesis by getting some structure of representation of Riemann zeta-function by. 9 thg 7, 2021. I'll try to summarize my understanding of the manuscript (). Products and services. Then we demonstrate that such function can have singularities only for Re s = 1/n, where n is a non-zero natural number. Subjects: General Mathematics (math. Every so often, a new mathematician arrives on the scene having developed a working proof to. it was announced that Hideya Matsumoto had found a proof, . Nov 06, 2022 · PDF | This is a straightforward approach to study the Riemann hypothesis by getting some structure of representation of Riemann zeta-function by. There has been a paper doing rounds on Facebook for the past several days, claiming a proof of the Riemann hypothesis. Finding a proof has been the holy grail of number theory since Riemann first published his hypothesis. In order to prove this result we introduce a compact representation of algebraic integers which allows. Hatem Fayed. Back in the 1960s, Atiyah and collaborator. Submission history From: Hatem Fayed [ view email ]. × Close Log In. Authors: Hatem Fayed (Submitted on 5 Sep 2022 , revised 24 Oct 2022 (this version, v2), latest version 27 Oct 2022 ). Some time around 2016, Prof. Cite as: arXiv:2209. Riemann Hypothesis: All nontrivial zeros are on the line Re s =. In this article, we will prove Riemann Hypothesis by using the mean value theorem of integrals. Timothy Gowers said: “As far as I can see, the idea that the Riemann hypothesis has some bearing on cryptography is based on a fantasy that if we could prove the Riemann hypothesis, we’d get. The extended Riemann hypothesis asserts that for every number field K and every complex number s with ζ K ( s) = 0: if the real part of s is between 0 and 1, then it is in fact 1/2. Sep 26, 2018 · “The Riemann hypothesis has been proved, unless you’re the type of person who doesn’t believe in proof by contradiction,” he said during his talk. The function Ξ ( t) := ξ ( 1 2 + i t), ξ ( s) := s ( s − 1) 2 π − s / 2 Γ ( s 2) ζ ( s), serves as a proxy to the ζ -function, because as it says here,. Subjects: General Mathematics (math. Then, through three theorems, we showed that in the critical line all zeros of the $\xi(s)$ function are simple, all local maxima are positive and all local minima are negative. Prime numbers , or those whose only factors are 1 and itself — such as 2, 3, 5 and 7— don't seem to follow. We’ll begin by studying infinite series of complex numbers and complex functions as. GM] for this version). If f is continuous on that interval. The hypothesis states that all of the nontrivial zeros of the Riemann zeta function are located on the critical line. Thus, the Riemann Hypothesis is completely true. Very strong experimental evidence. Keywords Riemann Hypothesis (RH) · Proof · Completed zeta function. Any mathematician looking to become a millionaire can do so; all they need is to offer a definitive proof of the Riemann Hypothesis. A senior lecturer at the Federal University in Oye. The proof is relatively easy with the appropriate geometric machinery (for example, it’s left as an exercise in Hartshorne’s book Algebraic Geometry ). Michael Atiyah, a prominent mathematician emeritus at the University of Edinburgh, announced yesterday (Sept. The most famous quandary, the Riemann hypothesis, is perhaps the greatest unsolved question in mathematics, with the Clay Mathematics Institute offering a $1 million prize for a correct. Abstract and Figures. 24 thg 5, 2019. Mohamed Mustafa Rabie. Abstract. Re (ζ (1/2 + it ), Im (ζ (1/2 + it) is plotted with t ranging between −30 and 30. Mathematician who solved prime-number riddle claims new breakthrough. the Arthur-Merlin class AM if the generalized Riemann hypothesis holds true, while the best known upper bound in positive character-istic remains PSPACE. Brierly Ph. Then, all non-trivial zeros of Riemann zeta-function are proved to have real part equal to 1 2. Products and services. Of the ten trillion (give or take) found so far, all of them seem to have a real part of exactly 1/2. 5 thg 3, 2021. If f is continuous on that interval. Then, all non-trivial zeros of Riemann zeta-function are proved to have real part equal to 1 2. It has been proven that there an infinite number of non-trivial zeros. Finally, using the functional equation, we reduce these possibilities to Re s = 1/2 only. org/millennium/Rules_etc/ ) for proof of the Riemann hypothesis. In this article, we will prove Riemann Hypothesis by using the mean value theorem of integrals. Riemann hypothesis stands proved in three different ways. 11 thg 2, 2020. The breakthrough are new important properties of the Riemann zeta . The proof depends on a new function T(s), the Todd function, named by Hirzebruch after my teacher J. Hinter den Riemann Hypothesis in Characteristic p in Historical Perspective. Mathematician who solved prime-number riddle claims new breakthrough. This book tells the story of the Riemann hypothesis for function fields (or curves) starting with Artin's 1921 thesis, covering Hasse's work in the 1930s on elliptic fields and more, and concluding with Weil's final proof in 1948. Riemann hypothesis stands proved in three different ways. The Riemann hypothesis controls (in some statistical sense) the distribution of primes, and one can prove stronger results about the running time of various number-theoretic algorithms if one knows that RH (or some its generalizations) are true. Subjects: General Mathematics (math. Your claim would suggest that 99% of mathematics is advanced math, which is a crazy scale. Of the ten trillion (give or take) found so far, all of them seem to have a real part of exactly 1/2. The Riemann hypothesis, stating that the real part of all non-trivial zero points fo the zeta function must be , is one of the most important unproven hypothesises in number theory. In a report published in 1859, Riemann stated that this might very well be a general fact. The proof cannot be read as an isolated argument. The Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers ("trivial zeros") and the complex numbers 1 2 + i t for real t. With some complex analysis you can proof that there is a continuous (actually holomorphic if you know what it means) extension of the function so that it is defined in whole C. I show a proof of the Riemann Hypothesis by proving the truth of Robin's inequality with a generating function approach. org e-Print archive. At present, the most we know is that at. Download Free PDF. Sep 05, 2022 · Hatem Fayed. To this day Riemann's hypothesis about the non-trivial zeros of the Riemann zeta function remains unsolved, despite extensive research by numerous great mathematicians for hundreds of years. 28 thg 5, 2013. zeta(s)=1/2 sin πs. The Riemann Hypothesis (RH) has been aroundfor more than 140. I want to use th. The Derivation of The Riemann Zeta Function from. His latest claim has lead to a press release from Purdue. THE DEDEKIND ZETA FUNCTION. Whereas the prime number theorem gives an estimate of the number of primes below n for any n, the Riemann hypothesis bounds the error in that estimate: At worst, it grows like √ n log n. If f is continuous on that interval. Cite as: arXiv:2209. A proof that it is true for every interesting solution would shed light on many of the mysteries surrounding the distribution of prime numbers. The Derivation of The Riemann Zeta Function from. The best conceptual work on this subject is probably still the proof of Gauss’ prime number theorem (another related conjecture by Riemann’s advisor) by Hadamard and de la Vallée-Poussain in the late 19th century. In order to prove this result we introduce a compact representation of algebraic integers which allows. The Riemann Hypothesis or RH, is a millennium problem, that has remained unsolved for the last 161 years. A 🧵 on the Riemann hypothesis and Yitang Zhang's latest preprint on the Landau-Siegel zeros conjecture, which I covered yesterday. In the case of curves, there is also a more elemen-tary proof due to Bombieri. So, what What is the hypothesis? Why has the search for a proof become something of a holy grail for mathematicians?. 8 thg 3, 2022. Besides being one of the great unsolved problems in mathematics and therefore garnishing glory for the person who solves it, the Riemann hypothesis is one of the Clay Mathematics Institute's. This provides some evidence for the more general conjecture that all zeta functions associated with automorphic forms satisfy a Riemann hypothesis, which includes the classical Riemann hypothesis as a special case. Riemann can make some scientists "!!2!!" to walk in another way,It's similar to the right way. We present a short and simple proof of the Riemann’s Hypothesis (RH) where only undergraduate mathematics is needed. One of the most famous unsolved problems in mathematics likely remains unsolved. Proof of the Riemann hypothesis is number 8 of Hilbert's problems and number 1 of Smale's problems. The extended Riemann hypothesis asserts that for every number field K and every complex number s with ζ K ( s) = 0: if the real part of s is between 0 and 1, then it is in fact 1/2. GM] (or arXiv:2209. Nov 04, 2022 · One strategy for the proof of the Riemann hypothesis is what is known as the Hilbert-Pólya conjecture. GM) MSC classes: 11M26. The present preprint completes the arXiv preprint # 2202. It's generally considered that a proof of the Riemann hypothesis will be very useful in computer science, especially cryptography. The Riemann hypothesis is a conjecture about the Riemann zeta function. The function is introduced by Riemann, which zeros are identical equal to non-trivial zeros of zeta function. abstract:- in this paper we use analytic continuation of the riemann zeta function to conclude that all the zeros lie on the critical line, < (s) = 1/2. “People usually accept proof by. Only an abstract proof will do. Other two proofs are derived using Eulers formula and elementary algebra. What will it take to prove the Riemann hypothesis? Various mathematicians have made some amount of headway toward a proof. The Derivation of The Riemann Zeta Function from. Riemann hypothesis stands proved in three different ways. Kumar Eswaran posted a claimed proof of the Riemann Hypothesis online. 01890v4 [math. The hypothesis states that all of the nontrivial zeros of the Riemann zeta function are located on the critical line. videos of lap dancing
Riemann Hypothesis(1) January 25, 2023 January 26, 2023 by ShuoXu. . Riemann hypothesis proof
It was identified by Hilbert in 1900 as one of his 23 mathematical challenges for the 20th Century, and by the Clay Mathematics Institute in 2000 as one of its seven $1million Millennium Prize Problems. Analytically continuing gamma and zeta function to an extended domain, poles and. For almost 160 years, the Riemann hypothesis has been one of mathematics most famous unsolved problems. In this module we’ll learn about power series representations of analytic functions. Dec 17, 2011 · The Riemann hypothesis is that all of the other zeros lay on the dotted line, Re (s)=1/2. The first 4 pages of that preprint were devoted to a set of necessary reminders, given in a very concise way: we here give a self-contained, fully developed, version of this part. In this article, it is proved that the non-trivial zeros of the Riemann zeta function must lie on the critical line, known as the Riemann hypothesis. The Riemann hypothesis is so difficult that the person who eventually proves it (or disproves it!) will probably need to invent whole new mathematical concepts, idioms, functions. 1 Introduction Zeros of the derivatives of the Riemann zeta function $\zeta$(s) have been studied for about 80 years. Nov 06, 2022 · PDF | This is a straightforward approach to study the Riemann hypothesis by getting some structure of representation of Riemann zeta-function by. This checked version was submitted to a. This aspect is in some. Riemann can make some. Analytically continuing gamma and zeta function to an extended domain, poles and. Nov 06, 2022 · PDF | This is a straightforward approach to study the Riemann hypothesis by getting some structure of representation of Riemann zeta-function by. The Riemann hypothesis has been of great interest in the mathematics community since it was proposed by Bernhard Riemann in 1859, and makes important implications about the distribution of prime numbers. Cite as: arXiv:2209. Robin [19, Théorème 1] improved Ramanujan’s result by showing the following equivalence. I was particularly amused by the line about discovering a "scientific technique for detecting and tracking someone on. Proof of Riemann Hypothesis. In 2000, the Clay Mathematics Institute ( http://www. Only an abstract proof will do. Now there are multiple proofs. 00000000000 for a complex numbers. In this module we’ll learn about power series representations of analytic functions. Riemann Hypothesis(1) January 25, 2023 January 26, 2023 by ShuoXu. Real values are shown on the horizontal axis and imaginary values are on the vertical axis). With some complex analysis you can proof that there is a continuous (actually holomorphic if you know what it means) extension of the function so that it is defined in whole C. In a letter to Andrew Odlyzko, dated January 3, 1982, George Pólya said that while he was in Göttingen around 1912 to 1914 he was asked by Edmund Landau for a physical reason that the Riemann hypothesis should be true, and suggested that this would be the case if the imaginary parts t of the zeros. Last night a preprint by Xian-Jin Li appeared on the arXiv, claiming a proof of the Riemann Hypothesis. Part (3) was proved by André Weil in the 1940's; parts (1) and (2) were proved much earlier. Whereas the prime number theorem gives an estimate of the number of primes below n for any n, the Riemann hypothesis bounds the error in that estimate: At worst, it grows like √ n log n. 01890 [math. Answer (1 of 5): Below are four ways you can tell if a bounded function f on an interval [a,b] is Riemann integrable besides using the definition. some persons' proof of Riemann Hypothesis):. Riemann can make some scientists "!!2!!" to walk in another way,It's similar to the right way. zeta(s)=1/2 sin πs. Did Michael Atiyah solve the Riemann. Feb 04, 2017 · The Riemann hypothesis is an unproven statement referring to the zeros of the Riemann zeta function. Michael Atiyah, a prominent mathematician emeritus at the University of Edinburgh, announced yesterday (Sept. One of the most famous unsolved problems in mathematics likely remains unsolved. First, we briefly reviewed the simplified Riemann function and its important properties. A year or so ago, he remarked in passing, "Bro, in my view, philosophy is a bit overrated! You. Translate PDF. Nov 06, 2022 · PDF | This is a straightforward approach to study the Riemann hypothesis by getting some structure of representation of Riemann zeta-function by. So I. It is the last remaining statement which has not been resolved is the Riemann Hypothesis. the assumption that the Riemann hypothesis is true, Ramanujan [18] showed that the inequality σ(n)<eγnloglogn holds for all sufficiently large positive integers n. GM) MSC classes: 11M26. Riemann’s hypothesis is equivalent to the positivity of the quadratic form QW(φ) ≥ 0 for any φ ∈ C∞ c(0, + ∞). A proof of Riemann's hypothesis with Fourier transform. Proceeding by contradiction, the author wants to show that. Products and services. In this paper, I will prove the Riemann Hypothesis without violating any mathematical rules or laws. Riemann hypothesis stands proved in three different ways. A proof of the Riemann hypothesis would have far-reaching consequences for number theory and for the use of primes in cryptography. Timothy Gowers said: “As far as I can see, the idea that the Riemann hypothesis has some bearing on cryptography is based on a fantasy that if we could prove the Riemann hypothesis, we’d get. Jul 02, 2008 · Posted on July 2, 2008 by woit. Published in 1859, it is a fascinating piece of mathematical conjecture. Before we begin, you should know that I’m not actually going to present a proof of the Riemann Hypothesis. 3 compilation (2019)https://istotne-nagr. However, I doubt that this question will be resolved before the GUE hypothesis itself is settled. Proposition1 (Robin) The Riemann hypothesis is true if and only if σ(n)<eγnloglogn. It was identified by Hilbert in 1900 as one of his 23 mathematical challenges for the 20th Century, and by the Clay Mathematics Institute in 2000 as one of its seven $1million Millennium Prize Problems. It was identified by Hilbert in 1900 as one of his 23 mathematical challenges for the 20th Century, and by the Clay Mathematics Institute in 2000 as one of its seven $1million Millennium Prize Problems. 01890v4 [math. 17 hours ago · Yitang (Tom) Zhang, a Chinese-American mathematician who recently revealed that he had solved the Landau-Siegel zeros conjecture, delivered an online speech at Peking University on November 8 to answer external questions on his newly published 111-page paper. Analytically continuing gamma and zeta function to an extended domain, poles and. Nov 06, 2022 · PDF | This is a straightforward approach to study the Riemann hypothesis by getting some structure of representation of Riemann zeta-function by. Primes-based security is based on the belief that finding one of the two prime factors of an appropriately-generated semiprime is difficult. Most mathematicians consider calculus to be lower-level because students still have not been able to prove anything mathematically significant by that level. However, these results above marked a huge step in the theory of prime numbers. Any mathematician looking to become a millionaire can do so; all they need is to offer a definitive proof of the Riemann Hypothesis. And it's not clear how far away such a proof. “People usually accept proof by. In the late 1940s, H. Analytically continuing gamma and zeta function to an extended domain, poles and. Submission history From: Hatem Fayed [ view email ]. Riemann hypothesis stands proved in three different ways. Given that evidence, most mathematicians think the Riemann hypothesis is true. A new proof of the Riemann Hypothesis. It was identified by Hilbert in 1900 as one of his 23 mathematical challenges for the 20th Century, and by the Clay Mathematics Institute in 2000 as one of its seven $1million Millennium Prize Problems. There are three important properties that we would like to have: (1) rationality, (2) satisfies a functional equation, and (3) satisfies an analogue of the Riemann hypothesis. Given that evidence, most mathematicians think the Riemann hypothesis is true. Hatem Fayed. THE DEDEKIND ZETA FUNCTION. I was unable to find any issue with the proof (Edit: see the answer by Winther), but maybe these notes will help someone in following the argument and forming their own opinion. Robin [19, Théorème 1] improved Ramanujan’s result by showing the following equivalence. 5 thg 9, 2022. At present, the most we know is that at. By now over 1. Besides being one of the great unsolved problems in mathematics and therefore garnishing glory for the person who solves it, the Riemann hypothesis is one of the Clay Mathematics Institute's. Sep 05, 2022 · Hatem Fayed. In this article, we will prove Riemann Hypothesis by using the mean value theorem of integrals. Also see this question: Would a proof of the Riemann hypothesis affect security? RH has numerous implications for regularity in the distribution of primes. However, there is no proof that really all nontrivial zeros lie on this line and this conjecture is called the Riemann Hypothesis. In this module we’ll learn about power series representations of analytic functions. To prove Riemann hypothesis from the functional equation concept of delta function is introduced similar to gamma and pi function. ashkiller14 • 19 hr. ashkiller14 • 19 hr. | Find, read and cite all the research you need. . ukraine telegram group war, emily ratajkowski sextape, cartoon japanese porn, bbc dpporn, eveo premium dual monitor stand, skipthegames com, gay pinoy chupa, sarah jessie porn, masajes near me, bravo pornos, tyga leaked, happy ending massage nj co8rr