Proceedings of the Japan Academy, Series A, Mathematical Sciences

Euler products beyond the boundary for Selberg zeta functions

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.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 90, Number 8 (2014), 101-106.

Dates
First available in Project Euclid: 3 October 2014

https://projecteuclid.org/euclid.pja/1412341992

Digital Object Identifier
doi:10.3792/pjaa.90.101

Mathematical Reviews number (MathSciNet)
MR3266742

Zentralblatt MATH identifier
1259.35175

Subjects
Primary: 11M06: $\zeta (s)$ and $L(s, \chi)$

Citation

Koyama, Shin-ya; Suzuki, Fumika. Euler products beyond the boundary for Selberg zeta functions. Proc. Japan Acad. Ser. A Math. Sci. 90 (2014), no. 8, 101--106. doi:10.3792/pjaa.90.101. https://projecteuclid.org/euclid.pja/1412341992

References

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