On the index of fractions with square-free denominators in arithmetic progressions

被引：0

作者：

Emre Alkan

Andrew H. Ledoan

Marian Vâjâitu

Alexandru Zaharescu

机构：

[1] University of Illinois at Urbana-Champaign,Department of Mathematics

[2] Romanian Academy,“Simion Stoilow” Institute of Mathematics

来源：

The Ramanujan Journal | 2008年 / 16卷

关键词：

Index of Farey fractions; Square-free integers; Riemann zeta-function and Dirichlet ; -functions; Arithmetic progressions; 11B57; 11M06; 11N25;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We prove asymptotic formulas for the first and second moments of the index of fractions with square-free denominators of order Q streaming in a given arithmetic progression as Q→∞.

引用

页码：131 / 161

页数：30

共 50 条

[21] On Square-Free Numbers
Grabowski, Adam
[J]. FORMALIZED MATHEMATICS, 2013, 21 (02): : 153 - 162
[22] ON SQUARE-FREE DIVISORS
GIOIA, AA
VAIDYA, AM
[J]. AMERICAN MATHEMATICAL MONTHLY, 1965, 72 (04): : 454 - &
[23] SQUARE-FREE INTEGERS
CHOWLA, S
SMITH, RA
VAIDYA, AM
[J]. AMERICAN MATHEMATICAL MONTHLY, 1964, 71 (06): : 686 - &
[24] Some results in square-free and strong square-free edge-colorings of graphs
Sudeep, K. S.
Vishwanathan, Sundar
[J]. DISCRETE MATHEMATICS, 2007, 307 (14) : 1818 - 1824
[25] Rich square-free words
Vesti, Jetro
[J]. THEORETICAL COMPUTER SCIENCE, 2017, 687 : 48 - 61
[26] ON THE PRODUCT OF SQUARE-FREE WORDS
DELUCA, A
[J]. DISCRETE MATHEMATICS, 1984, 52 (2-3) : 143 - 157
[27] Square-free partial words
Halava, Vesa
Harju, Tero
Karki, Tomi
[J]. INFORMATION PROCESSING LETTERS, 2008, 108 (05) : 290 - 292
[28] DISTRIBUTION OF SQUARE-FREE NUMBERS
HOOLEY, C
[J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1973, 25 (06): : 1216 - 1223
[29] Square-free perfect graphs
Conforti, M
Cornuéjols, G
Vuskovic, K
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 2004, 90 (02) : 257 - 307
[30] The distance to square-free polynomials
Dubickas, Arturas
Sha, Min
[J]. ACTA ARITHMETICA, 2018, 186 (03) : 243 - 256

← 1 2 3 4 5 →