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arXiv · 2108.13868

Sharp bound for the fourth moment of holomorphic Hecke cusp forms

Peter Zenz
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Abstract

We prove that the fourth moment of holomorphic Hecke cusp forms is bounded provided that the Riemann Hypothesis holds for an appropriate degree 8 L-function. We accomplish this using Watson's formula, which translates the question in hand into a moment problem for L-functions which is amenable to the techniques of Soundararajan and Harper on obtaining sharp bounds for moments of the Riemann zeta function.

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Peter Zenz. 2021-08-31. Sharp bound for the fourth moment of holomorphic Hecke cusp forms. https://arxiv.org/abs/2108.13868

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