2003/10/31 by Samuel Grushevsky, Riccardo Salvati Manni
Mathematics · #math.NT #math.CO
published as Mathemtics Research Letters 12 (2005) · final version, to appear
arxiv created 2005/09/18 · arxiv updated 2009/12/01
In this paper we generalize the famous Jacobi's triple product identity, considered as an identity for theta functions with characteristics and their derivatives, to higher genus/dimension. By applying the results and methods developed in our previous paper math.AG/0310085 several generalizations to Siegel modular forms are obtained. These generalizations are identities satisfied by theta functions with characteristics and their derivatives at zero. Equating the coefficients of the Fourier expansion of these relations to zero yields non-trivial combinatorial identities.