Description
Abstract: The sup-norm problem asks for good upper bounds on the size of $L^2$-normalised eigenfunctions. In the setting of automorphic forms on $\mathrm{GL}_2$ the most studied case are spherical Hecke-Maaß newforms of level $N$. Only very recently an in depth study of non-spherical Hecke-Maaß forms was taken up by Blomer-Harcos-Maga-Milićević. As an $p$-adic analogue of this we replace newforms by forms that lie in a small $p$-adic $K$-type. We can prove non-trivial sup-norm bounds on average over a basis of this $K$-type when its dimension grows. In this talk we will make this statement precise and discuss some aspects of its proof.
The link for the talk is https://zoom.us/j/94752830725, the password is the order of $\mathrm{SL}_2(\mathbb{F}_{97})$.