On fourth and higher moments of short exponential sums related to cusp forms

JOURNAL OF NUMBER THEORY

卷:218

Article

Ernvall-Hytonen, Anne-Maria^1,2  Vesalainen, Esa V.^1,2 

[1] Abo Akad Univ, Math & Stat, Domkyrkotorget 1, Turku 20500, Finland

[2] Univ Helsinki, Dept Math & Stat, POB 68,Pietari Kalmin Katu 5, FI-00014 Helsinki, Finland

关键词: Holomorphic cusp forms;    Exponential sums;    Moments;    Large values;    Truncated Voronoi identity;   

DOI  :  10.1016/j.jnt.2020.07.012

来源: Elsevier

【 摘 要 】

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. We obtain the conjectured best possible bound in the case of the fourth moment. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free