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

 

Two new proofs of Lerch's functional equation


Author: Bruce C. Berndt
Journal: Proc. Amer. Math. Soc. 32 (1972), 403-408
MSC: Primary 10H05
MathSciNet review: 0297721
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Abstract: One bright Sunday morning I went to church, And there I met a man named Lerch. We both did sing in jubilation, For he did show me a new equation.

Two simple derivations of the functional equation of

$\displaystyle \sum\limits_{n = 0}^\infty {\exp [2\pi inx]{{(n + a)}^{ - s}}} $

are given. The original proof is due to Lerch.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0297721-3
PII: S 0002-9939(1972)0297721-3
Keywords: Lerch's zeta-function, Hurwitz zeta-function, Riemann zeta-function, functional equation, Euler-Maclaurin summation formula
Article copyright: © Copyright 1972 American Mathematical Society