4 problems

Let $p$ be prime, let $r\in(\frac{1}{p+1},\frac{p}{p+1})$, and let $h$ be an $r$-overconvergent modular function on the region $X_0(1)_{\ge p^{-r}}$. Its spectral expansion is the…

Let $p\in\{2,3,5\}$, let $r$ range over some open interval containing $\frac{1}{2}$, and let $\mathcal{S}_k(r)$ be the space on which the overconvergent $U$ operator acts. A factor…

Nearly-overconvergent universal eigenform conjecture. There is an affinoid neighbourhood

Let $b_n$ be the coefficient of the $n$-th basis vector in the Kolberg-basis expansion of $h=\iota^*(\Theta_1^{-1}\mathcal{F}^{[\mathfrak{p}_1]})$. Coefficient-bound conjecture. On…