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Sharp Bound for the Fourth Moment of Holomorphic Hecke Cusp Forms
International Mathematics Research Notices ( IF 1 ) Pub Date : 2022-07-28 , DOI: 10.1093/imrn/rnac199
Peter Zenz

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

中文翻译:

全纯 Hecke 尖点形式的第四个矩的锐界

我们证明如果广义黎曼假设成立,则全纯 Hecke 尖点形式的第四矩受一个常数的限制。我们使用 Watson 的公式来实现这一点,该公式将手头的问题转换为 $L$ 函数的矩问题,该问题适用于 Soundararajan 和 Harper 的技术,以获得 Riemann zeta 函数的矩的锐界。
更新日期:2022-07-28
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