The sup-norm problem beyond the newform

Abstract

In this note we take up the classical sup-norm problem for automorphic forms and view it from a new angle. Given a twist minimal automorphic representation $\pi$ we consider a special small $G{L}_2({\mathbb{Z}}_p)$-type $V$ in $\pi$ and proof global sup-norm bounds for an average over an orthonormal basis of $V$. We achieve a non-trivial saving when the dimension of $V$ grows.

29 pages, 1 table; v2: revised version incorporating suggestions by a referee

References in corpus (2)

• Beyond the spherical sup-norm problem
• A remark on conductor, depth and principal congruence subgroups