On the summation of the singular series
type: Item
instance of: scholarly article
title: On the summation of the singular series
zbMATH Open document ID: 0623.10036
DOI: 10.1007/BF01168672
author: B. George
published in: Manuscripta Mathematica
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155206
review text: This paper deals with explicit evaluation, in certain cases, of \(r(n, \mathrm{gen}\,I_k)\) which denotes the average number of representations of \(n\) by the genus of \(I_k\), the identity quadratic form in \(k\) variables. The methods rely heavily on Siegel's formula for this quantity in terms of \(p\)-adic densities. The author uses Gauss sums to evaluate the 2-adic density in the cases she considers. She obtains the classical results of Ramanujan for sums of 24 squares and the results of Bateman when \(k=3\) or 4.
reviewed by: James Lee Hafner
Mathematics Subject Classification ID: 11P05
Mathematics Subject Classification ID: 11E12
Mathematics Subject Classification ID: 11E45
zbMATH DE Number: 4010620
zbMATH Keywords: sum of squares
zbMATH Keywords: singular series
zbMATH Keywords: average number of representations
zbMATH Keywords: quadratic form
zbMATH Keywords: Siegel's formula
zbMATH Keywords: p-adic densities
zbMATH Keywords: Gauss sums
zbMATH Keywords: 2-adic density
MaRDI profile type: Publication
cites work: Arithmetic behaviour of the sums of three squares
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cites work: Q5779465
cites work: Explicit formula of the traces of Hecke operators for \(\Gamma_0(N)\)
cites work: Q5625265
cites work: On modular forms of half integral weight
OpenAlex ID: W1989955495
description: scientific article; zbMATH DE number 4010620