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.

arXiv comment29 pages, 1 table; v2: revised version incorporating suggestions by a referee

References in corpus (11)

• The subconvexity problem for $\GL_{2}$
• A conjecture on Whittaker-Fourier coefficients of cusp forms
• Bounding sup-norms of cusp forms of large level
• On the computation of local components of a newform
• Hybrid sup-norm bounds for Maass newforms of powerful level
• On the size of p-adic Whittaker functions
• The sup-norm problem for GL(2) over number fields
• Local bounds for $L^p$ norms of Maass forms in the level aspect
• Beyond the spherical sup-norm problem
• Sup norms of newforms on $G{L}_2$ with highly ramified central character
• A remark on conductor, depth and principal congruence subgroups