Large values of modular forms

2012/07/25 by Templier, Nicolas
#11F41 #11F70 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1207.6134

Abstract

We show that there are primitive holomorphic modular forms f of weight two and arbitrary large level N such that |f(z)| ≫ 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).

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