On the $p$-adic periods of the modular curve $X({\Gamma }_0(p)\cap \Gamma (2))$

Abstract

We prove a variant of Oesterlé's conjecture about $p$-adic periods of the modular curve $X_0(p)$, with an additional $\Gamma (2)$-structure. We use de Shalit's techniques and $p$-adic uniformization of curves whose reduction is semi-stable.

22 pages