The Fourier expansion of η(z)η(2z)η(3z)/η(6z)

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.

10 pages. Version 2: Section 4 was added

Cited by in corpus (1)

• Complete determination of the zeta function of the Hilbert scheme of $n$ points on a two-dimensional torus