Two generalizations of Jacobi's derivative formula

Details Two generalizations of Jacobi's derivative formula Two generalizations of Jacobi's derivative formula

2003-10-08

arxiv.org/abs/math/0310106v2

Mathemtics Research Letters 12 (2005)

Mathematics

Number Theory

final version, to appear

Scientific paper

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.

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