Tsukuba Journal of Mathematics

A formula for the Hurwitz zeta function, Riemann's functional equation and certain integral representations

Yasuyuki Kachi and Pavlos Tzermias

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Abstract

There is a well-known formula for the Hurwitz zeta function which implies the functional equation for the Riemann zeta function. We give a new proof of that formula and recover certain integral representations for the Hurwitz and Riemann zeta functions.

Article information

Source
Tsukuba J. Math., Volume 42, Number 2 (2018), 309-334.

Dates
First available in Project Euclid: 2 April 2019

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1554170427

Digital Object Identifier
doi:10.21099/tkbjm/1554170427

Mathematical Reviews number (MathSciNet)
MR3934993

Zentralblatt MATH identifier
07055235

Subjects
Primary: 11M06: $\zeta (s)$ and $L(s, \chi)$ 11M35: Hurwitz and Lerch zeta functions
Secondary: 44A15: Special transforms (Legendre, Hilbert, etc.)

Keywords
Hurwitz zeta function Riemann zeta function functional equation Laplace-Mellin transform integral representations

Citation

Kachi, Yasuyuki; Tzermias, Pavlos. A formula for the Hurwitz zeta function, Riemann's functional equation and certain integral representations. Tsukuba J. Math. 42 (2018), no. 2, 309--334. doi:10.21099/tkbjm/1554170427. https://projecteuclid.org/euclid.tkbjm/1554170427


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