Primes with an average sum of digits

被引：36

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
HEATHBROWN, DR
[J]. 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
KATAI, I
[J]. ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE, 1977, 30 (1-2): : 169 - 173
[15] DISTRIBUTION OF DIGITS OF PRIMES IN Q-ARY CANONICAL FORM
KATAI, I
[J]. 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
SHIOKAWA, I
[J]. PROCEEDINGS OF THE JAPAN ACADEMY, 1974, 50 (08): : 551 - 554

← 1 2 3 →