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.
Citation
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
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