ULTRAFRIABLE INTEGERS IN ARITHMETIC PROGRESSIONS

被引：0

作者：

Dartyge, Cecile ^{[1
]}

Feutrie, David ^{[1
]}

Tenenbaum, Gerald ^{[1
]}

机构：

[1] Univ Lorraine, Inst Elie Cartan, BP 70239, F-54506 Vandoeuvre Les Nancy, France

来源：

QUARTERLY JOURNAL OF MATHEMATICS | 2022年 / 73卷 / 01期

关键词：

LARGE PRIME FACTORS; SMOOTH NUMBERS;

D O I：

10.1093/qmath/haab025

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A natural integer is called y-ultrafriable if none of the prime powers occurring in its canonical decomposition exceed y. We investigate the distribution of y-ultrafriable integers not exceeding x among arithmetic progressions to the modulus q. Given a sufficiently small, positive constant epsilon, we obtain uniform estimates valid for q <= y(c/log2 y) whenever log y <= (log x)(epsilon), and for q <= root y if (log x)(2+epsilon) <= y <= x.

引用

页码：149 / 174

页数：26

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