THE DISTRIBUTION OF SMOOTH NUMBERS IN ARITHMETIC PROGRESSIONS

被引：0

作者：

BALOG, A ^{[1
]}

POMERANCE, C ^{[1
]}

机构：

[1] UNIV GEORGIA,DEPT MATH,ATHENS,GA 30602

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1992年 / 115卷 / 01期

关键词：

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We estimate the number of integers n up to x in the arithmetic progression a (mod q) with n free of prime factors exceeding y . For a wide range of the variables x, y, q, and a we show that this number is about x/(qu(u)), where u = log x/log y.

引用

页码：33 / 43

页数：11

共 50 条

[21] SMALLEST SQUAREFREE NUMBERS IN ARITHMETIC PROGRESSIONS
WARLIMONT, R
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1971, 250 : 99 - +
[22] ON EXISTENCE OF PRIME NUMBERS IN ARITHMETIC PROGRESSIONS
KOSHIBA, Z
UCHIYAMA, S
[J]. PROCEEDINGS OF THE JAPAN ACADEMY, 1966, 42 (07): : 696 - &
[23] DISTRIBUTION OF MOMENTS OF HURWITZ CLASS NUMBERS IN ARITHMETIC PROGRESSIONS AND HOLOMORPHIC PROJECTION
Kane, Ben
Pujahari, Sudhir
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2023, 376 (08) : 5503 - 5519
[24] Valuations, arithmetic progressions, and prime numbers
Seki, Shin-ichiro
[J]. NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, 2018, 24 (04) : 128 - 132
[25] Arithmetic Progressions Among Powerful Numbers
Chan, Tsz Ho
[J]. JOURNAL OF INTEGER SEQUENCES, 2023, 26 (01)
[26] NOTICE ON SQUAREFREE NUMBERS IN ARITHMETIC PROGRESSIONS
FLUCH, W
[J]. MONATSHEFTE FUR MATHEMATIK, 1976, 82 (04): : 269 - 274
[27] PRIME NUMBERS IN CERTAIN ARITHMETIC PROGRESSIONS
Murty, M. Ram
Thain, Nithum
[J]. FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 2006, 35 (01) : 249 - 259
[28] Distribution of divisors in arithmetic progressions
de la Bretèche, R
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2000, 32 : 257 - 262
[29] DISTRIBUTION OF SEQUENCES IN ARITHMETIC PROGRESSIONS
FOUVRY, E
[J]. ACTA ARITHMETICA, 1982, 41 (04) : 359 - 382
[30] Moments of the distribution of k$k$-free numbers in short intervals and arithmetic progressions
Nunes, Ramon M.
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2022, 54 (04) : 1282 - 1298

← 1 2 3 4 5 →