Theta constants identities for Jacobians of cyclic 3-sheeted covers of the sphere and representations of the symmetric group

Details Theta constants identities for Jacobians of cyclic 3-sheeted covers of the sphere and representations of the symmetric group Theta constants identities for Jacobians of cyclic 3-sheeted covers of the sphere and representations of the symmetric group

2007-04-08

arxiv.org/abs/0704.1032v1

Mathematics

Complex Variables

7 pages

Scientific paper

We find identities between theta constants with rational characteristics evaluated at period matrix of $R,$ a cyclic 3 sheeted cover of the sphere with $3k$ branch points $\lambda_1...\lambda_{3k}.$ These identities follow from Thomae formula \cite{BR}. This formula expresses powers of theta constants as polynomials in $\lambda_1...\lambda_{3k}.$ We apply the representation of the symmetric group to find relations between the polynomials and hence between the associated theta constants.

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