Asymptotic formula for the convolution of a generalized divisor function

被引：1

作者：

Bykovskii, V. A. ^{[1
]}

Frolenkov, D. A. ^{[1
]}

机构：

[1] Russian Acad Sci, Far Eastern Branch, Inst Appl Math, Khabarovsk Branch, Khabarovsk 680000, Russia

来源：

DOKLADY MATHEMATICS | 2015年 / 92卷 / 03期

基金：

俄罗斯科学基金会;

关键词：

Asymptotic Behavior; Asymptotic Formula; DOKLADY Mathematic; Riemann Zeta Function; Analytic Number Theory;

D O I：

10.1134/S1064562415060071

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An asymptotic formula is obtained for the sum of terms sigma (it) (n)sigma(-it) (N - n) (t is real) over 0 < n < N with a remainder estimated by O (epsilon)((1+|t|)(1+epsilon) N (3/4+epsilon)) for any epsilon > 0. As a consequence, Porter's result on a power scale for the average number of steps in the Euclidean algorithm is improved.

引用

页码：670 / 673

页数：4

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