Bulletin of the Belgian Mathematical Society - Simon Stevin

Euler's constants for the Selberg and the Dedekind zeta functions

Yasufumi Hashimoto,Yasuyuki Iijima,Nobushige Kurokawa, and Masato Wakayama

Full-text: Open access

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.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin Volume 11, Number 4 (2004), 493-516.

Dates
First available: 10 December 2004

Permanent link to this document
http://projecteuclid.org/euclid.bbms/1102689119

Mathematical Reviews number (MathSciNet)
MR2115723

Zentralblatt MATH identifier
02186490

Subjects
Primary: 11M06: $\zeta (s)$ and $L(s, \chi)$ 11M36: Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. Explicit formulas

Keywords
Euler's constant Selberg zeta function Dedekind zeta function

Citation

Hashimoto, Yasufumi; Iijima, Yasuyuki; Kurokawa, Nobushige; Wakayama, Masato. Euler's constants for the Selberg and the Dedekind zeta functions. Bulletin of the Belgian Mathematical Society - Simon Stevin 11 (2004), no. 4, 493--516. http://projecteuclid.org/euclid.bbms/1102689119.


Export citation