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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


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.


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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.


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

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

Primary: 11M06 , 11M36

Keywords: Dedekind zeta function , Euler's constant , Selberg zeta function

Rights: Copyright © 2004 The Belgian Mathematical Society


Vol.11 • No. 4 • November 2004
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