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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Easy proofs of Riemann’s functional equation for $\zeta (s)$ and of Lipschitz summation
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by Marvin Knopp and Sinai Robins PDF
Proc. Amer. Math. Soc. 129 (2001), 1915-1922 Request permission

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
  • Tom M. Apostol, Introduction to analytic number theory, Undergraduate Texts in Mathematics, Springer-Verlag, New York-Heidelberg, 1976. MR 0434929
  • Julian Bonder, Über die Darstellung gewisser, in der Theorie der FlĂźgelschwingungen auftretender Integrale durch Zylinderfunktionen, Z. Angew. Math. Mech. 19 (1939), 251–252 (German). MR 42, DOI 10.1002/zamm.19390190409
  • Lipschitz, R. Untersuchung der Eigenschaften einer Gattung von undendlichen Reihen. J. Reine und Angew. Math., 127-156, 1889.
  • Hans Rademacher, Topics in analytic number theory, Die Grundlehren der mathematischen Wissenschaften, Band 169, Springer-Verlag, New York-Heidelberg, 1973. Edited by E. Grosswald, J. Lehner and M. Newman. MR 0364103
  • Bruno Schoeneberg, Elliptic modular functions: an introduction, Die Grundlehren der mathematischen Wissenschaften, Band 203, Springer-Verlag, New York-Heidelberg, 1974. Translated from the German by J. R. Smart and E. A. Schwandt. MR 0412107
  • H. M. Stark, Dirichlet’s class-number formula revisited, A tribute to Emil Grosswald: number theory and related analysis, Contemp. Math., vol. 143, Amer. Math. Soc., Providence, RI, 1993, pp. 571–577. MR 1210543, DOI 10.1090/conm/143/01022
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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
  • MR Author ID: 342098
  • Email: srobins@math.temple.edu
  • Received by editor(s): November 5, 1999
  • Published electronically: February 2, 2001
  • Communicated by: Dennis A. Hejhal
  • © Copyright 2001 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 1915-1922
  • MSC (2000): Primary 11M35, 11M06
  • DOI: https://doi.org/10.1090/S0002-9939-01-06033-6
  • MathSciNet review: 1825897