Theta constants identities for Jacobians of cyclic 3-sheeted covers of the sphere and representations of the symmetric group
Abstract
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 λ1...λ3k. These identities follow from Thomae formula BR. This formula expresses powers of theta constants as polynomials in λ1...λ3k. 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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