The Divisor Function in Arithmetic Progressions to Smooth Moduli

被引：14

作者：

Irving, Alastair James ^{[1
]}

机构：

[1] Univ Oxford, Math Inst, Oxford OX2 6GG, England

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2015年 / 2015卷 / 15期

基金：

英国工程与自然科学研究理事会;

关键词：

AVERAGE VALUE; SUMS;

D O I：

10.1093/imrn/rnu149

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

By using the q-analog of van der Corput's method, we study the divisor function in an arithmetic progression to modulus q. We show that the expected asymptotic formula holds for a larger range of q than was previously known, provided that q has a certain factorization.

引用

页码：6675 / 6698

页数：24

共 50 条

[1] TERNARY DIVISOR FUNCTIONS IN ARITHMETIC PROGRESSIONS TO SMOOTH MODULI
Xi, Ping
MATHEMATIKA, 2018, 64 (03) : 701 - 729
[2] General divisor functions in arithmetic progressions to large moduli
Fei Wei
BoQing Xue
YiTang Zhang
Science China Mathematics, 2016, 59 : 1663 - 1668
[3] General divisor functions in arithmetic progressions to large moduli
WEI Fei
XUE BoQing
ZHANG YiTang
Science China(Mathematics), 2016, 59 (09) : 1663 - 1668
[4] General divisor functions in arithmetic progressions to large moduli
Wei Fei
Xue BoQing
Zhang YiTang
SCIENCE CHINA-MATHEMATICS, 2016, 59 (09) : 1663 - 1668
[5] On the restricted divisor function in arithmetic progressions
Shparlinski, Igor E.
REVISTA MATEMATICA IBEROAMERICANA, 2012, 28 (01) : 231 - 238
[6] Divisor function, inequalities and arithmetic progressions
Cimadevilla Villacorta, Jorge Luis
INTERNATIONAL JOURNAL OF NUMBER THEORY, 2018, 14 (08) : 2225 - 2238
[7] THE DIVISOR FUNCTION OVER ARITHMETIC PROGRESSIONS
FOUVRY, E
IWANIEC, H
ACTA ARITHMETICA, 1992, 61 (03) : 271 - 287
[8] Squarefree Integers in Arithmetic Progressions to Smooth Moduli
Mangerel, Alexander P.
FORUM OF MATHEMATICS SIGMA, 2021, 9
[9] THE DIVISOR FUNCTION IN ARITHMETIC PROGRESSIONS MODULO PRIME POWERS
Khan, Rizwanur
MATHEMATIKA, 2016, 62 (03) : 898 - 908
[10] THE DIVISOR PROBLEM FOR ARITHMETIC PROGRESSIONS
FRIEDLANDER, JB
IWANIEC, H
ACTA ARITHMETICA, 1985, 45 (03) : 273 - 277

← 1 2 3 4 5 →