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

Adel Betina, Emmanuel Lecouturier

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 un…