Modular equations of order $p$ and Theta functions
An algorithm to obtain equations between theta functions with integral characteristics evaluated at $τ$ and $pτ$ for $g>1$ is presented.
math.CV↗
arXiv subjects
Yaacov Kopeliovich
Publications and source records attributed to Yaacov Kopeliovich.
Theta constants identities for Jacobians of cyclic 3-sheeted covers of the sphere and representations of the symmetric group
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 $λ_1...λ_{3k}.$ These identities follow from Thomae formula \cite{BR}. This formula expresses powers of theta constants as polynomials in $λ_1...λ_{3k}.$ We apply the representation of the symmetric group to find relations between the polynomials and hence between the associated theta constants.
math.CV↗