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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Marvin Knopp and Sinai Robins
Journal: Proc. Amer. Math. Soc. 129 (2001), 1915-1922
MSC (2000): Primary 11M35, 11M06
Published electronically: February 2, 2001
MathSciNet review: 1825897
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Abstract | References | Similar Articles | Additional Information

Abstract:

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 $\zeta(s)$.


References [Enhancements On Off] (What's this?)

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Additional Information

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: http://dx.doi.org/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
Published electronically: February 2, 2001
Communicated by: Dennis A. Hejhal
Article copyright: © Copyright 2001 American Mathematical Society