On Fourth and Higher Moments of Short Exponential Sums Related to Cusp Forms
Anne-Maria Ernvall-Hyt\"onen, Esa V. Vesalainen
TL;DR
This paper establishes upper bounds for the fourth and higher moments of short exponential sums involving Fourier coefficients of holomorphic cusp forms, especially when twisted by rational additive characters with small denominators.
Contribution
It provides new bounds for higher moments of exponential sums related to cusp forms, extending previous results to more complex moments and twists.
Findings
Upper bounds for fourth moments of exponential sums
Extension to higher moments of these sums
Results applicable to small denominator rational twists
Abstract
We obtain upper bounds for the fourth and higher moments of short exponential sums involving Fourier coefficients of holomorphic cusp forms twisted by rational additive twists with small denominators.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.