English

Large values of modular forms

Number Theory 2013-09-23 v4 Representation Theory

Abstract

We show that there are primitive holomorphic modular forms f of weight two and arbitrary large level N such that f(z)N1/4|f(z)| \gg N^{1/4} for some point z. Thereby we disprove a folklore conjecture that the sup-norm of such forms would be as small as No(1)N^{o(1)}.

Keywords

Cite

@article{arxiv.1207.6134,
  title  = {Large values of modular forms},
  author = {Nicolas Templier},
  journal= {arXiv preprint arXiv:1207.6134},
  year   = {2013}
}
R2 v1 2026-06-21T21:41:38.730Z