Prime geodesic theorem for the Picard manifold

被引：5

作者：

Balkanova, Olga ^{[1
]}

Frolenkov, Dmitry ^{[2
]}

机构：

[1] Chalmers Univ Technol, Dept Math Sci, Chalmers Tvargata 3, S-41296 Gothenburg, Sweden

[2] Russian Acad Sci, Steklov Math Inst, 8 Gubkina St, Moscow 119991, Russia

来源：

ADVANCES IN MATHEMATICS | 2020年 / 375卷

关键词：

Spectral exponential sum; Prime geodesic theorem; Picard manifold; FORMULA; SUBCONVEXITY;

D O I：

10.1016/j.aim.2020.107377

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let Gamma = PSL(2,Z vertical bar i vertical bar) be the Picard group and H-3 be the three-dimensional hyperbolic space. We study the Prime Geodesic Theorem for the quotient Gamma\H-3, called the Picard manifold, obtaining an error term of size O(X3/2+theta/2+epsilon), where theta denotes a subconvexity exponent for quadratic Dirichlet L-functions defined over Gaussian integers. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：42

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