The Riemann zeta function can be thought of as describing a landscape with the positions of the zeros as features of the landscape. So 2*S2=. ( Log Out / Regularization is a choice. The calculation uses the wave functions that act as what we call smoothing functions in mathematics and we find the famous $\sum n=\frac{-1}{12}=\zeta(-1)$ as a proportionnality factor for the amplitude of the force. So it seems like a toy model or exercise. But when you read his source, extract below, you get this: Mathematicians have long suspected that there might be a way to convert the Riemann hypothesis into an equation similar to those used in quantum physics. > Is this a correct proof of the Riemann Hypothesis. JavaScript is disabled. So get another source, or another answer from this site...Without Riemann, building directly on the work of Gauss, we would not have General Relativity, but that was because his work was, Prime numbers are directly related to quantum physics, en.wikipedia.org/wiki/Look-and-say_sequence#Cosmological_Decay, Creating new Help Center documents for Review queues: Project overview, Feature Preview: New Review Suspensions Mod UX, Role of physics in the zeta function $\zeta$ and the Riemann hypothesis, Hamiltonian related to Riemann zeta function, Applications of the Spectral Theorem to Quantum Mechanics. Proving that the sum of the sequence is equal to 1/2. If you pretend these were drawn from a random variable and calculate the correlations, you get the same result as if you just took a random Hermitian matrix like the kind that is used to model heavy nuclei. /Filter /FlateDecode /Length 1685 Must I bring those other passports whenever I use the BNO one? 3.) Why does Ray Bradbury use "flounder" for an action with a positive outcome? There is another integral formula that works for all domain, and can be simplified to the series sum which you descibe, also, it simplifies to bernoulli numbers resulting 0's of negative even integers. For a better experience, please enable JavaScript in your browser before proceeding. Why echo request doesn't show in tcpdump? If you look closely at this question it is extremely similar to the previous one. 1 0 obj << Oddly enough this is just 4 times S3. >> endobj Now to prove the problem we started of with, 1+2+3+4+… Let this = S3. Change ). /Length 2600 Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. And one more thing guys, Happy New Year!! The Physics of the Riemann Zeta function Abstract: One of the Clay Institute’s Millennium Prize Problems is the Riemann Hypothesis. This is not to say that there are no connections/applications of Riemann Zeta to physics. I don't think the infinite series converges that you have written down, so you have to find another representation of the function in that region to do any math anyway. Incidentally, I found this post that has a few more examples, including the two above. What crimes have been committed or attempted in space? However, they have been used to suggest answers to some other long-standing and important problems relating to the zeta function. The sum depends on the term you stop at. That formula only works in a limited range, and only in places with trivial zeros. You can look up this as it was known as Montgomery's pair correlation conjecture. Many times these claims of connections are tenuous at best, but there is undoubtedly deep connections between higher math and physics - definitely more than just vector calc, diff eq's, and linear algebra. And primes are vital to cryptography and therefore to the ever-burgeoning world of online commerce and security. The hypothesis is that, apart from some trivial exceptions, all of the zeros of this function lie on a straight line (known as the critical line). This is of central importance in mathematics because the Riemann zeta function encodes information about the prime numbers — the atoms of arithmetic. 1-S1=1-[1-1+1-1…] which is 1-S=1-1+1-1… Hence 1-S1=S1 and so 2S1=1. /Contents 3 0 R There is a good paper that goes over some of the ways in which this function is used in physics: Physics of the Riemann Hypothesis. What I mean is that if you stop at an odd term you will get your answer to be 1, whereas if you stop at an even number your sum will be 0. The infinite series is the zeta function. But it seems obviously wrong. Can someone re-license my project under a different license, Mystery game from 2000s set on an island with a bell. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. Let the sum of this sequence = S2. Wait… that means 2S2=S1. JavaScript is disabled. This formula confirmed the number 42. What does the real and imaginary part in the domain and range of zeta mean physically? Some basic zeta functions In this section we will construct analytical continuations of basic zeta func-tions. /Filter /FlateDecode It should output zero when the real part is 1/2 (for all imaginary parts). But apparently it stayed at the curiosity stage and deeper examination showed discrepancies with the current knowledge. It only takes a minute to sign up. The infinite series is the zeta function. Then you look at the normalized differences between neighboring zeroes. Meanwhile, number theorists Conrey and Gonek had suggested the next moment in the series. Thread starter pivoxa15; Start date Mar 24, 2006 Mar 24, 2006 Hurwitz zeta function. /MediaBox [0 0 612 792]