Generalized Dedekind sums and equidistribution mod 1

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• 作者：Claire Burrin ^{claire.burrin@math.ethz.ch" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Automorphic forms ; Dedekind eta function ; Dedekind sums ; Kloosterman sums ; Fuchsian group ; Equidistribution
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：172
• 期：Complete
• 页码：270-286
• 全文大小：348 K

文摘

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)$\mathrm{SL}(2,\mathbb{Z})$. We present a compatible notion of Dedekind sums, which we name Dedekind symbols, for any non-cocompact lattice Γ<SL(2,R)$\mathrm{\Gamma }<\mathrm{SL}(2,\mathbb{R})$, 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.