Open Access
July 2016 Refinement of prime geodesic theorem
Shin-ya Koyama
Proc. Japan Acad. Ser. A Math. Sci. 92(7): 77-81 (July 2016). DOI: 10.3792/pjaa.92.77


We prove existence of a set $E$ of positive real numbers, which is relatively small in the sense that its logarithmic measure is finite, such that we can improve the error term of the prime geodesic theorem as $x\to\infty$ $(x\notin E)$. The result holds for any compact hyperbolic surfaces, and it would also be true for generic hyperbolic surfaces of finite volume according to the philosophy of Phillips and Sarnak.


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Shin-ya Koyama. "Refinement of prime geodesic theorem." Proc. Japan Acad. Ser. A Math. Sci. 92 (7) 77 - 81, July 2016.


Published: July 2016
First available in Project Euclid: 21 July 2016

zbMATH: 06673656
MathSciNet: MR3529088
Digital Object Identifier: 10.3792/pjaa.92.77

Primary: 11F72
Secondary: 11M41

Keywords: arithmetic groups , prime geodesic theorem , Selberg zeta functions

Rights: Copyright © 2016 The Japan Academy

Vol.92 • No. 7 • July 2016
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