Proceedings of the American Mathematical Society

Easy proofs of Riemann's functional equation for $\zeta (s)$ and of Lipschitz summation

Author(s): Marvin Knopp; Sinai Robins
Journal: Proc. Amer. Math. Soc. 129 (2001), 1915-1922.
MSC (2000): Primary 11M35, 11M06
Posted: February 2, 2001
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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 $\zeta(s)$ .

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11M35, 11M06

Marvin Knopp
Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122

Sinai Robins
Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
Email: srobins@math.temple.edu

DOI: 10.1090/S0002-9939-01-06033-6
PII: S 0002-9939(01)06033-6
Keywords: Poisson summation, Lipschitz summation, Eisenstein series, Riemann zeta function, Hurwitz zeta function
Received by editor(s): November 5, 1999
Posted: February 2, 2001
Communicated by: Dennis A. Hejhal
Copyright of article: Copyright 2001, American Mathematical Society

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