Euler products beyond the boundary for Selberg zeta functions

Shin-ya Koyama, Fumika Suzuki

Type: Article

Publication Date: 2014-08-01

Citations: 4

DOI: https://doi.org/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.

Locations

Proceedings of the Japan Academy Series A Mathematical Sciences - View - PDF

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