3 problems

Let $\mathcal{L}(f)$ denote the $\mathcal{L}$-invariant of a $p$-new modular Hecke eigenform of level $\Gamma_0(p)$. Bergdall--Pollack's equidistribution conjecture. As the weight…

Let $f$ be an admissible newform of weight $k>2$ and level $\Gamma_0(p)$, and suppose that $p$ splits completely in its Hecke field $K_f$. Write $\varepsilon(f)$ for its Atkin--Leh…

Let $g$ be a modular form, let $p$ be a prime, let $\mathcal{L}_{g_\alpha}$ be the associated $p$-adic $L$-invariant, and let $u_{g_\alpha}$ be the Gross–Stark unit attached to…