On the p-adic periods of X...(p).
We study a certain finitely generated multiplicative subgroup of the Hilbert class field of a quartic CM field. It consists of special values of certain theta functions of genus 2 and is analogous to the group of Siegel units. Questions of integrality of these specials values are related to the arithmetic of the Siegel moduli space.
Let be the Jacobian of the modular curve associated with and the one associated with . We study as a Hecke and Galois-module. We relate a certain matrix of -adic periods to the infinitesimal deformation of the -operator.
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