2002•Communications of the Korean Mathematical SocietyRequires access

NOTES ON SOME IDENTITIES INVOLVING THE RIEMANN ZETA FUNCTION

Hyerim Lee, Bo-Myoung Ok, Junesang Choi

Abstract

We first review Ramaswami's find 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 ζ(s) and Apostol's identities given here.

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Key concepts: Mathematics, Riemann zeta function, Arithmetic zeta function, Riemann hypothesis, Pure mathematics, Particular values of Riemann zeta function, Prime zeta function, Series (stratigraphy)