Large values of modular forms

Nicolas Templier

Type: Article

Publication Date: 2014-01-01

Citations: 26

DOI: https://doi.org/10.4310/cjm.2014.v2.n1.a3

Abstract

We show that there are primitive holomorphic modular forms f of weight two and arbitrary large level N such that $|f(z)| \gg N^{1/4}$ for some point z. Thereby we disprove a folklore conjecture that the sup-norm of such forms would be as small as $N^{o(1)}$.

Locations

Cambridge Journal of Mathematics - View - PDF
arXiv (Cornell University) - View - PDF

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