Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2002; 17(1): 165-173

Printed March 1, 2002

Copyright © The Korean Mathematical Society.

Notes on some identities involving the Riemann Zeta function

Hyerim Lee, Bo Myoung Ok, and Junesang Choi

Pusan National University, Youngsan University, Dongguk University

Abstract

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We first review Ramaswami's and Apostol's identities involving the Zeta function in a rather detailed manner. We then present corrected, or generalized formulas, or a different method of proof for some of them. We also give closed-form evaluation of some series involving the Riemann Zeta function by an integral representation of $\zeta(s)$ and Apostol's identities given here.

Keywords: Bernoulli numbers and polynomials, Riemann and Hurwitz Zeta functions, Harmonic numbers, Pochhammer symbol, M\"obius function

MSC numbers: Primary 11M06; Secondary 33C05

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