A basis for \(S_k(\Gamma_0(4))\) and representations of integers as sums of squares
type: Item
instance of: scholarly article
title: A basis for \(S_k(\Gamma_0(4))\) and representations of integers as sums of squares
zbMATH Open document ID: 1280.11021
author: Shinji Fukuhara
author: Yifan Yang
published in: The Ramanujan Journal
publication date: 2012-09-20T00:00:00Z
review text: In an earlier paper [Math. Proc. Camb. Philos. Soc. 146, No. 2, 321--350 (2009; Zbl 1205.11052)] the authors gave a basis for the space \(S_{k}(\Gamma_{0}(2))\) of cusp forms of even weight \(k\) for the congruence subgroup \(\Gamma_{0}(2)\) in terms of normalized Eisenstein series. This paper does the same for \(S_{k}(\Gamma_{0}(4))\) and applies the results to obtain formulas for the generating function of \(r_{4s}(n)\), the number of representations of \(n\) as a sum of \(4s\) integral squares.
reviewed by: Tom M. Apostol
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 11E25
Mathematics Subject Classification ID: 11F30
Mathematics Subject Classification ID: 11F67
zbMATH DE Number: 6084534
zbMATH Keywords: modular forms (one variable)
zbMATH Keywords: period polynomials
zbMATH Keywords: Fourier coefficients of modular forms
zbMATH Keywords: sum of squares
MaRDI profile type: Publication
full work available at URL: s11139-011-9341-y
OpenAlex ID: W2004564356
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DOI: 10.1007/S11139-011-9341-Y
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description: scientific article; zbMATH DE number 6084534