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Let [Formula: see text] be a function such that [Formula: see text] as [Formula: see text]. Let [Formula: see text] be the [Formula: see text]th Hecke eigenvalue of a fixed… Click to show full abstract
Let [Formula: see text] be a function such that [Formula: see text] as [Formula: see text]. Let [Formula: see text] be the [Formula: see text]th Hecke eigenvalue of a fixed holomorphic cusp form [Formula: see text] for [Formula: see text]. We show that for any real-valued function [Formula: see text] such that [Formula: see text], mean values of [Formula: see text] over intervals [Formula: see text] are bounded by [Formula: see text] for all but [Formula: see text] many integers [Formula: see text], in which [Formula: see text] is the average value of [Formula: see text] over primes. We generalize this for [Formula: see text] for [Formula: see text].
Journal Title: International Journal of Number Theory
Year Published: 2021
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