On the set of divisors of Gaussian integers

被引：0

作者：

Maier, Helmut ^{[1
]}

Singh, Saurabh Kumar ^{[1
,2
]}

机构：

[1] Univ Ulm, Inst Number Theory & Probabil Theory, D-89069 Ulm, Germany

[2] Indian Stat Inst, Stat Math Unit, 203 BT Rd, Kolkata 700108, India

来源：

RAMANUJAN JOURNAL | 2019年 / 50卷 / 02期

关键词：

Gaussian integers; Divisor function; Erdos conjecture on divisor function;

D O I：

10.1007/s11139-019-00158-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In Maier and Tenenbaum (Invent Math 76(1):121-128, 1984), Tenenbaum and the first author proved an old conjecture of Paul Erdos about the propinquity of divisors of integers. In this paper, we prove an analogous results for Gaussian integers.

引用

下载

页码：355 / 366

页数：12

共 50 条

[31] ON DIVISORS OF SUMS OF INTEGERS .4.
SARKOZY, A
STEWART, CL
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1988, 40 (04): : 788 - 816
[32] SUMS OF IMAGINARY POWERS OF DIVISORS OF INTEGERS
HALL, RR
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1975, 9 (36): : 571 - 580
[33] The distribution law of divisors on a sequence of integers
Daoud, Mohamed Saber
Hidri, Afef
Naimi, Mongi
LITHUANIAN MATHEMATICAL JOURNAL, 2015, 55 (04) : 474 - 488
[34] On consecutive integers divisible by the number of their divisors
Andreescu, Titu
Luca, Florian
Phaovibul, M. Tip
ACTA ARITHMETICA, 2016, 173 (03) : 269 - 281
[35] Integers with dense divisors (Part 2)
Saias, E
JOURNAL OF NUMBER THEORY, 2001, 86 (01) : 39 - 49
[36] Distribution laws of the divisors of friable integers
Drappeau, Sary
Tenenbaum, Gerald
MATHEMATISCHE ZEITSCHRIFT, 2018, 288 (3-4) : 1299 - 1326
[37] Gaussian Integers
Futa, Yuichi
Okazaki, Hiroyuki
Mizushima, Daichi
Shidama, Yasunari
FORMALIZED MATHEMATICS, 2013, 21 (02): : 115 - 125
[38] The number of prime factors of integers with dense divisors
Weingartner, Andreas
JOURNAL OF NUMBER THEORY, 2022, 239 : 57 - 77
[39] TITCHMARSCH DIVISORS OF INTEGERS WITH NO LARGE PRIME FACTOR
FOUVRY, E
TENENBAUM, G
LECTURE NOTES IN MATHEMATICS, 1990, 1434 : 86 - 102
[40] NUMBER OF LARGE PRIME DIVISORS OF CONSECUTIVE INTEGERS
GALAMBOS, J
JOURNAL OF NUMBER THEORY, 1977, 9 (03) : 338 - 341

← 1 2 3 4 5 →