A simple modular proof of Farkas' arithmetic identity modulo 4
type: Item
instance of: scholarly article
title: A simple modular proof of Farkas' arithmetic identity modulo 4
zbMATH Open document ID: 1221.11104
author: W. Raji
published in: Missouri Journal of Mathematical Sciences
publication date: 2009-02-12T00:00:00Z
review text: The author uses results of \textit{D. L. Vestal} jun. from [Rocky Mt. J. Math. 31, No. 2, 687--696 (2001; Zbl 0982.11020)] which use generalized Dedekind \(\eta\)-functions to represent the basis of~\(M_2(\Gamma_0(4))\) and a theorem of Jacobi on representation numbers of sums of two squares to give a simple new derivation of an identity first proved by \textit{H. Farkas} [Complex analysis and dynamical systems II, Contemp. Math. 382, 121--130 (2005; Zbl 1176.11013)], which relates the Fourier coefficients of modular Eisenstein series of weight~2 for \(\Gamma_0(4)\) and the difference between number of divisors of integers which are congruent to~1 and to~3 modulo~4.
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 11F20
zbMATH DE Number: 5507337
zbMATH Keywords: modular forms
zbMATH Keywords: modular functions
zbMATH Keywords: eta products
zbMATH Keywords: generalized eta products
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5507337