Products of Small Integers in Residue Classes and Additive Properties of Fermat Quotients

被引：6

作者：

Harman, Glyn ^{[1
]}

Shparlinski, Igor E. ^{[2
]}

机构：

[1] Univ London, Royal Holloway, Dept Math, Egham TW20 0EX, Surrey, England

[2] Univ New S Wales, Dept Pure Math, Sydney, NSW 2052, Australia

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2016年 / 2016卷 / 05期

关键词：

CHARACTER SUMS; EXPONENTIAL-SUMS; SHORT INTERVALS; VALUE SET; DIVISIBILITY; MODULO; PRIME;

D O I：

10.1093/imrn/rnv182

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that for any epsilon > 0 and a sufficiently large cube-free q, any reduced residue class modulo q can be represented as a product of 14 integers from the interval [1, q(1/4e1/2+epsilon)]. The length of the interval is at the lower limit of what is possible before the Burgess bound on the smallest quadratic nonresidue is improved. We also consider several variations of this result and give applications to Fermat quotients.

引用

页码：1424 / 1446

页数：23

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