On character sums with determinants

作     者：Etienne Fouvry Igor E.Shparlinski Étienne Fouvry;Igor E.Shparlinski

作者机构：CNRSLaboratoire de Mathématiques d'OrsayUniversité Paris-SaclayOrsay 91405France School of Mathematics and StatisticsUniversity of New South WalesSydneyNSW 2052Australia 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2023年第66卷第12期

页      面：2693-2714页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported in part by the Australian Research Council (Grant No. DP200100355)。 

主　　题：character sum determinant Burgess bound 

摘      要：We estimate weighted character sums with determinants ad-bc of 2×2 matrices modulo a prime p with entries a,b,c and d vary ing over the interval [1,N].Our goal is to obtain non-trivial bounds for values of N as small as possible.In particular,we achieve this goal,with a power saving,for N≥p^(1/8+ε) with any fixed ε0,which is very likely to be the best possible unless the celebrated Burgess bound is improved,By other techniques,we also treat more general sums but sometimes for larger values of N.