The Fourier expansion of $$\varvec{\eta (z)\eta (2z)\eta (3z)/\eta (6z)}$$ |
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Authors: | Christian Kassel Christophe Reutenauer |
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Institution: | 1.Institut de Recherche Mathématique Avancée,CNRS & Université de Strasbourg,Strasbourg,France;2.Mathématiques,Université du Québec à Montréal,Montréal,Canada |
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Abstract: | We compute the Fourier coefficients of the weight one modular form \(\eta (z)\eta (2z)\eta (3z)/\eta (6z)\) in terms of the number of representations of an integer as a sum of two squares. We deduce a relation between this modular form and translates of the modular form \(\eta (z)^4/\eta (2z)^2\). In the last section we use our main result to give an elementary proof of an identity by Victor Kac. |
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