English

The sup-norm problem for GL(2) over number fields

Number Theory 2024-11-18 v2

Abstract

We solve the sup-norm problem for spherical Hecke-Maass newforms of square-free level for the group GL(2) over a number field, with a power saving over the local geometric bound simultaneously in the eigenvalue and the level aspect. Our bounds feature a Weyl-type exponent in the level aspect, they reproduce or improve upon all known special cases, and over totally real fields they are as strong as the best known hybrid result over the rationals.

Keywords

Cite

@article{arxiv.1605.09360,
  title  = {The sup-norm problem for GL(2) over number fields},
  author = {Valentin Blomer and Gergely Harcos and Péter Maga and Djordje Milićević},
  journal= {arXiv preprint arXiv:1605.09360},
  year   = {2024}
}

Comments

40 pages, LaTeX2e; v2: revised version incorporating suggestions by the referee, to appear in JEMS

R2 v1 2026-06-22T14:13:10.144Z