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October 2014 Euler products beyond the boundary for Selberg zeta functions
Shin-ya Koyama, Fumika Suzuki
Proc. Japan Acad. Ser. A Math. Sci. 90(8): 101-106 (October 2014). DOI: 10.3792/pjaa.90.101

Abstract

Convergence of Euler products in the critical strip is directly related to a proof of the generalized Riemann hypothesis. Moreover its behavior on the critical line is called the deep Riemann hypothesis (DRH). Kimura-Koyama-Kurokawa recently proved DRH over function fields in case the $L$-function is regular at $s=1$ [3]. In this paper we generalize their results to Selberg zeta functions. Our results imply the DRH for principal congruence groups over function fields.

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Shin-ya Koyama. Fumika Suzuki. "Euler products beyond the boundary for Selberg zeta functions." Proc. Japan Acad. Ser. A Math. Sci. 90 (8) 101 - 106, October 2014. https://doi.org/10.3792/pjaa.90.101

Information

Published: October 2014
First available in Project Euclid: 3 October 2014

zbMATH: 1259.35175
MathSciNet: MR3266742
Digital Object Identifier: 10.3792/pjaa.90.101

Subjects:
Primary: 11M06

Keywords: Euler products , Riemann hypothesis , Selberg zeta functions

Rights: Copyright © 2014 The Japan Academy

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Vol.90 • No. 8 • October 2014
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