Mean square in the prime geodesic theorem

被引：12

作者：

Cherubini, Giacomo ^{[1
]}

Guerreiro, Joao ^{[1
]}

机构：

[1] Max Planck Inst Math, Bonn, Germany

来源：

ALGEBRA & NUMBER THEORY | 2018年 / 12卷 / 03期

关键词：

prime geodesic theorem; Selberg trace formula; Kuznetsov trace formula; Kloosterman sums; REFINEMENT;

D O I：

10.2140/ant.2018.12.571

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove upper bounds for the mean square of the remainder in the prime geodesic theorem, for every cofinite Fuchsian group, which improve on average on the best known pointwise bounds. The proof relies on the Selberg trace formula. For the modular group we prove a refined upper bound by using the Kuznetsov trace formula.

引用

页码：571 / 597

页数：27

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