Refinement of prime geodesic theorem

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Shin-ya Koyama¹ 

[1] Department of Biomedical Engineering, Toyo University

关键词: Prime geodesic theorem;    Selberg zeta functions;    arithmetic groups.;   

DOI  :  10.3792/pjaa.92.77

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

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.

【 授权许可】

Unknown