On the mean square of short exponential sums related to cusp forms
Anne-Maria Ernvall-Hyt\"onen
TL;DR
This paper estimates the average size of short exponential sums involving Fourier coefficients of holomorphic cusp forms, providing insights into their behavior and magnitude.
Contribution
It introduces a new method for estimating the mean square of short exponential sums related to cusp form Fourier coefficients.
Findings
Derived bounds for the mean square of the sums
Improved understanding of the distribution of Fourier coefficients
Potential applications to analytic number theory
Abstract
The purpose of the article is to estimate the mean square of a squareroot length exponential sum of Fourier coefficients of a holomorphic cusp form.
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Taxonomy
TopicsAnalytic Number Theory Research · Advanced Mathematical Identities · Advanced Algebra and Geometry