EXPONENTIAL SUM ESTIMATES OVER A SUBGROUP IN AN ARBITRARY FINITE FIELD

被引：19

作者：

Bourgain, J. ^{[1
]}

Glibichuk, A. ^{[2
]}

机构：

[1] Inst Adv Study, Princeton, NJ 08540 USA

[2] Univ Nacl Autonoma Mexico, Inst Matemat, Morelia 580899, Michoacan, Mexico

来源：

JOURNAL D ANALYSE MATHEMATIQUE | 2011年 / 115卷

关键词：

Arbitrary Element; Prime Order; Additive Character; Arbitrary Subset; Multiplicative Subgroup;

D O I：

10.1007/s11854-011-0023-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let F-q be the finite field consisting of q = p(r) elements and psi an additive character of the field F-q. Take an arbitrary multiplicative subgroup H of size vertical bar H vertical bar > q(C/(log log q)) for some constant C > 0 not largely contained in any multiplicative shift of a subfield. We show that vertical bar Sigma(h is an element of H) psi(h)vertical bar = o(vertical bar H vertical bar). This means that H is equidistributed in F-q.

引用

页码：51 / 70

页数：20

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