Dedekind sums and Fourier coefficients of modular forms
type: Item
instance of: scholarly article
title: Dedekind sums and Fourier coefficients of modular forms
zbMATH Open document ID: 0723.11018
DOI: 10.1016/0022-314X(90)90091-5
published in: Journal of Number Theory
publication date: 1990-01-01T00:00:00Z
review text: The result may be considered as a reasonably final answer for a sufficiently old (1972) question of H. Rademacher and E. Grosswald. Let for \(c\geq 1\) and \((d,c)=1\), S(d,c) be the Dedekind sum \(S(d,c)=\sum^{c-1}_{m=1}\{md/c\}\{m/c\}\), \(\{x\}=x-[x]-1/2\) if \(x\not\in {\mathbb{Z}}\) and \(\{x\}=0\) for \(x\in {\mathbb{Z}}\). Then for \(M\to +\infty\) \[ \frac{\log M}{M}\sum^{M}_{c=1}\frac{1}{c}\sum_{(d,c)=1}g(S(d,c),\frac{d}{c})=\frac{12}{\pi^ 2}\int^{\infty}_{- \infty}\int_{{\mathbb{R}}/{\mathbb{Z}}}g(x,y) dy dx+o(1) \] for each compactly supported continuous function g on \({\mathbb{R}}\times ({\mathbb{R}}/{\mathbb{Z}})\).
Mathematics Subject Classification ID: 11F20
Mathematics Subject Classification ID: 11F30
zbMATH DE Number: 4191779
zbMATH Keywords: modular forms
zbMATH Keywords: Kuznetsov's sum formula
zbMATH Keywords: Dedekind sum
author: Roelof Bruggeman
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4191779