关于整数矩阵除数函数余项的二次积分均值
Integral mean square estimation for the error term involving divisor functions of integer matrices
于若彤 1劳会学 1杨晓伟1
作者信息
- 1. 山东师范大学数学与统计学院,山东济南 250358
- 折叠
摘要
整数矩阵表法个数的渐近分布问题是解析数论中的重要研究课题,受到日益增长的关注.设t(2)3(n)是整数矩阵环 M2(Z)中形式为C=A1A2A3且|C|=n的矩阵表法个数的求和函数,Δ*2,3(X)是关于t(2)3(n)的渐近公式中的余项.利用经典的解析方法和黎曼zeta函数的良好性质,本文研究了整数矩阵除数函数t(2)3(n)在无平方因子数集上的分布问题,并得到了余项Δ*2,3(x)的二次积分均值的上界估计.
Abstract
The asymptotic behaviour of the number of representations of integer matri-ces is an important topic in analytic number theory,and has received increasing attention.Let t3(2)(n)be a summatory function of the number of representations of matrices from the ring of integer matrices M2(Z)in the form C=A1A2A3 with|C|=n.Denote byΔ*2,3(x)the error term of asymptotic formula related to t(2)3(n).Applying the classical analytic method and nice properties of the Riemann zeta function,this paper investigates the distribution of divisor functions of integer matrices t(2)3(n)on the square-free numbers and obtains the upper bounds for the integral mean square of error terms Δ*2,3(x).
关键词
余项/无平方因子数/整数矩阵除数函数Key words
error term/square-free number/divisor function of integer matrix引用本文复制引用
出版年
2024
NETL
NSTL
万方数据