On the average sum of the kth divisor function over values of quadratic polynomials

被引：1

作者：

Lapkova, Kostadinka ^{[1
]}

Zhou, Nian Hong ^{[2
]}

机构：

[1] Graz Univ Technol, Inst Anal & Number Theory, Kopernikusgasse 24-II, A-8010 Graz, Austria

[2] East China Normal Univ, Sch Math Sci, 500 Dongchuan Rd, Shanghai 200241, Peoples R China

来源：

RAMANUJAN JOURNAL | 2021年 / 55卷 / 03期

基金：

美国国家科学基金会; 奥地利科学基金会;

关键词：

Divisor functions; Quadratic polynomials; Circle method;

D O I：

10.1007/s11139-019-00240-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let F(x) is an element of Z[x(1), x(2), ... ,x(n)], n >= 3, be ann-variable quadratic polynomial with a nonsingular quadratic part. Using the circle method we derive an asymptotic formula for the sum S-k,S-F(X; B)= Sigma(x is an element of XB boolean AND Zn) tau(k) (F(x)); for X tending to infinity, where B subset of R-n is ann-dimensional box such that min(x is an element of XB) F(x) >= 0 for all sufficiently largeX, and tau(k)(center dot) is thekth divisor function for any integer k >= 2.

引用

页码：849 / 872

页数：24

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