Primes with an average sum of digits

被引：35

作者：

Drmota, Michael ^{[1
]}

Mauduit, Christian ^{[2
]}

Rivat, Joel ^{[2
]}

机构：

[1] Vienna Univ Technol, Inst Discrete Math & Geometry, A-1040 Vienna, Austria

[2] Univ Aix Marseille 2, Inst Math Luminy, CNRS, UMR 6206, F-13288 Marseille 9, France

来源：

COMPOSITIO MATHEMATICA | 2009年 / 145卷 / 02期

关键词：

sum-of-digits function; primes; exponential sums; central limit theorem; INTEGERS; NUMBERS; POWER;

D O I：

10.1112/S0010437X08003898

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The main goal of this paper is to provide asymptotic expansions for the numbers # {p <= x : p prime, s(q) (p) = k} for k close to ((q - 1)/2) log(q) X, where s(q)(n) denotes the q-ary sum-of-digits function. The proof is based on a thorough analysis of exponential sums of the form Sigma(p <= x) e(alpha S(q)(p)) (where the sum is restricted to p prime), for which we have to extend a recent result by the second two authors.

引用

页码：271 / 292

页数：22

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