Kloosterman sums in residue classes

被引：17

作者：

Blomer, Valentin ^{[1
]}

Milicevic, Djordje ^{[2
]}

机构：

[1] Math Inst, Bunsenstr 3-5, D-37073 Gottingen, Germany

[2] Max Planck Inst Math, D-53111 Bonn, Germany

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2015年 / 17卷 / 01期

基金：

欧洲研究理事会;

关键词：

Kloosterman sums; Kuznetsov formula; arithmetic progressions; Linnik's conjecture; SUBCONVEXITY PROBLEM; CUSP FORMS; EQUIDISTRIBUTION; COEFFICIENTS; CONJECTURE; LINNIK; MODULI; ZERO;

D O I：

10.4171/JEMS/498

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove upper bounds for sums of Kloosterman sums against general arithmetic weight functions. In particular, we obtain power cancellation in sums of Kloosterman sums over arithmetic progressions, which is of square-root strength in any fixed primitive congruence class up to bounds towards the Ramanujan conjecture.

引用

页码：51 / 69

页数：19

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