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.
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页码：670 / 673
页数：4
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