Distribution of values of Hardy sums over Chebyshev polynomials

被引：0

作者：

Wang, Jiankang ^{[1
]}

Xu, Zhefeng ^{[1
]}

Jia, Minmin ^{[1
]}

机构：

[1] Northwest Univ, Res Ctr Number Theory & Its Applicat, Xian 710127, Peoples R China

来源：

AIMS MATHEMATICS | 2024年 / 9卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Hardy sums; Chebyshev polynomials; values; DEDEKIND SUMS; MEAN-VALUE; FIBONACCI;

D O I：

10.3934/math.2024186

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper mainly studied the distribution of values of Hardy sums involving Chebyshev polynomials. By using the method of analysis and the arithmetic properties of Hardy sums and Chebyshev polynomials of the first kind, we obtained a sharp asymptotic formula for the hybrid mean value of Hardy sums S5(h, q) involving Chebyshev polynomials of the first kind. In addition, we also gave the value of Hardy sums S (h, q) and S3(h, q) involving Chebyshev polynomials. Finally, we found the reciprocal formulas of S3(h, q) and S4(h, q) involving Chebyshev polynomials of the first kind.

引用

页码：3788 / 3797

页数：10

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