Translator Disclaimer
November 2004 Euler's constants for the Selberg and the Dedekind zeta functions
Yasufumi Hashimoto, Yasuyuki Iijima, Nobushige Kurokawa, Masato Wakayama
Bull. Belg. Math. Soc. Simon Stevin 11(4): 493-516 (November 2004). DOI: 10.36045/bbms/1102689119

Abstract

The purpose of this paper is to study an analogue of Euler's constant for the Selberg zeta functions of a compact Riemann surface and the Dedekind zeta function of an algebraic number field. Especially, we establish similar expressions of such Euler's constants as de la Vall\'ee-Poussin obtained in 1896 for the Riemann zeta function. We also discuss, so to speak, higher Euler's constants and establish certain formulas concerning the power sums of essential zeroes of these zeta functions similar to Riemann's explicit formula.

Citation

Download Citation

Yasufumi Hashimoto. Yasuyuki Iijima. Nobushige Kurokawa. Masato Wakayama. "Euler's constants for the Selberg and the Dedekind zeta functions." Bull. Belg. Math. Soc. Simon Stevin 11 (4) 493 - 516, November 2004. https://doi.org/10.36045/bbms/1102689119

Information

Published: November 2004
First available in Project Euclid: 10 December 2004

zbMATH: 1080.11062
MathSciNet: MR2115723
Digital Object Identifier: 10.36045/bbms/1102689119

Subjects:
Primary: 11M06, 11M36

Rights: Copyright © 2004 The Belgian Mathematical Society

JOURNAL ARTICLE
24 PAGES


SHARE
Vol.11 • No. 4 • November 2004
Back to Top