Generalized Dedekind sums and equidistribution mod 1

JOURNAL OF NUMBER THEORY

卷:172

Article

Burrin, Claire¹ 

[1] ETH, Dept Math, Ramistr 101, CH-8092 Zurich, Switzerland

关键词: Automorphic forms;    Dedekind eta function;    Dedekind sums;    Kloosterman sums;    Fuchsian group;    Equidistribution;   

DOI  :  10.1016/j.jnt.2016.08.003

来源: Elsevier

【 摘 要 】

Dedekind sums are well-studied arithmetic sums, with values uniformly distributed mod 1. Based on their relation to certain modular forms, Dedekind sums may be defined as functions on the cusp set of SL(2, Z). We present a compatible notion of Dedekind sums, which we name Dedekind symbols, for any non-cocompact lattice Gamma < SL(2, R), and prove the corresponding equidistribution mod 1 result. The latter part builds up on a paper of Vardi, who first connected exponential sums of Dedekind sums to Kloosterman sums. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free