Year: 2026
Type: article
Abstract: In 1970, Apostol introduced the Möbius function of order k for an integer $k\ge 1$ . In 2001, it was generalized by Bege to the Möbius function $\mu _{k,m}$ of two parameters for any integers $m\ge k\ge 1$ . In this article, we will establish three kinds of asymptotic formulas related to $\mu _{k,m}$ for $m\ge k\ge 2$ in a unified elementary method. These formulas are related to the shifted convolution sums of Fourier coefficients of holomorphic cusp forms, Bergelson and Richter’s dynamical generalization of the prime number theorem, and the Titchmarsh divisor problem.
Source: Canadian Mathematical Bulletin
Author: Biao Wang
Institution: Yunnan University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W7128625311
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