The Sup-norm of Holomorphic Cusp Forms

2014/04/09 by Ye, Zhilin
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1404.2354

Abstract

Let f be a normalized holomorphic cusp form with a square-free level N and weight k. Using a pre-trace formula, we establish a sup-norm bound of f such that ‖y^kf(z)‖_∞ ≪ N^-1/6+ε where the trivial bound is ‖y^kf(z)‖_∞ ≪ 1. This result is an analog of a similar bound in Maaß form case.

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