EASY PROOFS OF RIEMANN’S FUNCTIONAL EQUATION FOR ζ(s) AND OF LIPSCHITZ SUMMATION
نویسندگان
چکیده
We present a new, simple proof, based upon Poisson summation, of the Lipschitz summation formula. A conceptually easy corollary is the functional relation for the Hurwitz zeta function. As a direct consequence we obtain a short, motivated proof of Riemann’s functional equation for ζ(s). Introduction We present a short and motivated proof of Riemann’s functional equation for Riemann’s zeta function ζ(s) = ∑∞ n=1 1 ns , initially defined in the half plane Re(s) > 1. In fact we prove the slightly more general functional relation for the Hurwitz zeta function ζ(s, a) = ∞ ∑
منابع مشابه
Riemann ’ s and ζ ( s )
[This document is http://www.math.umn.edu/ ̃garrett/m/complex/notes 2014-15/09c Riemann and zeta.pdf] 1. Riemann’s explicit formula 2. Analytic continuation and functional equation of ζ(s) 3. Appendix: Perron identity [Riemann 1859] exhibited a precise relationship between primes and zeros of ζ(s). A similar idea applies to any zeta or L-function with analytic continuation, functional equation, ...
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