Pretentious multiplicative functions and the prime number theorem for arithmetic progressions

被引：14

作者：

Koukoulopoulos, Dimitris ^{[1
]}

机构：

[1] Univ Montreal, Dept Math & Stat, Montreal, PQ H3C 3J7, Canada

来源：

COMPOSITIO MATHEMATICA | 2013年 / 149卷 / 07期

关键词：

prime number theorem for arithmetic progressions; multiplicative functions; Halasz's theorem; elementary proofs of the prime number theorem; Siegel's theorem; ZETA-FUNCTION;

D O I：

10.1112/S0010437X12000802

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Building on the concept of pretentious multiplicative functions, we give a new and largely elementary proof of the best result known on the counting function of primes in arithmetic progressions.

引用

页码：1129 / 1149

页数：21

共 50 条

[41] On the Least Prime in Some Arithmetic Progressions
蒙在照
数学进展, 1999, (06) : 543 - 544
[42] The Least Prime in Certain Arithmetic Progressions
Sabia, Juan
Tesauri, Susana
AMERICAN MATHEMATICAL MONTHLY, 2009, 116 (07): : 641 - 643
[43] ON EXISTENCE OF PRIME NUMBERS IN ARITHMETIC PROGRESSIONS
KOSHIBA, Z
UCHIYAMA, S
PROCEEDINGS OF THE JAPAN ACADEMY, 1966, 42 (07): : 696 - &
[44] Furstenberg systems of pretentious and MRT multiplicative functions
Frantzikinakis, Nikos
Lemanczyk, Mariusz
de la Rue, Thierry
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2025,
[45] ADDITIVE ARITHMETIC FUNCTIONS ON ARITHMETIC PROGRESSIONS
ELLIOTT, PDTA
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1987, 54 : 15 - 37
[46] Valuations, arithmetic progressions, and prime numbers
Seki, Shin-ichiro
NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, 2018, 24 (04) : 128 - 132
[47] Arithmetic progressions of prime-almost-prime twins
Tolev, DI
ACTA ARITHMETICA, 1999, 88 (01) : 67 - 98
[48] PRIME NUMBERS IN CERTAIN ARITHMETIC PROGRESSIONS
Murty, M. Ram
Thain, Nithum
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 2006, 35 (01) : 249 - 259
[49] Goldbach’s conjecture in arithmetic progressions: number and size of exceptional prime moduli
Claus Bauer
Archiv der Mathematik, 2017, 108 : 159 - 172
[50] Goldbach's conjecture in arithmetic progressions: number and size of exceptional prime moduli
Bauer, Claus
ARCHIV DER MATHEMATIK, 2017, 108 (02) : 159 - 172

← 1 2 3 4 5 →