Primes with an average sum of digits

被引：38

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

共 23 条

[11] PRIME-NUMBERS IN SHORT INTERVALS AND A GENERALIZED VAUGHAN IDENTITY [J].

HEATHBROWN, DR .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1982, 34 (06) :1365-1377

[12]

HOHEISEL G, 1930, SITZ PREUSS AKAD WIS, V33, P3

[13]

Iwaniec H., 2004, Amer. Math. Soc. Colloq. Publ., V53

[14] SUM OF DIGITS OF PRIMES [J].

KATAI, I .

ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE, 1977, 30 (1-2) :169-173

[15] DISTRIBUTION OF DIGITS OF PRIMES IN Q-ARY CANONICAL FORM [J].

KATAI, I .

ACTA MATHEMATICA HUNGARICA, 1986, 47 (3-4) :341-359

[16]

KATAI I, 1967, ANN U SCI BUDAP, V10, P89

[17]

Mauduit C, 1997, ACTA ARITH, V81, P145

[18]

MAUDUIT C, ANN MATH IN PRESS

[19]

MAUDUIT C, ACTA MATH IN PRESS

[20] SUM OF DIGITS OF PRIME NUMBERS [J].

SHIOKAWA, I .

PROCEEDINGS OF THE JAPAN ACADEMY, 1974, 50 (08) :551-554

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