The Fourier expansion of $\eta(z)\eta(2z)\eta(3z)/\eta(6z)$

Christian Kassel (1) , Christophe Reutenauer (2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 LaCIM - Laboratoire de combinatoire et d'informatique mathématique [Montréal]

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 $\eta(z)^4/\eta(2z)^2$.

Domaines: Théorie des nombres [math.NT]

Christian Kassel, Christophe Reutenauer. The Fourier expansion of $\eta(z)\eta(2z)\eta(3z)/\eta(6z)$. Archiv der Mathematik, 2017, 108, pp.453-463. ⟨10.1007/s00013-017-1033-4⟩. ⟨hal-01291833⟩