Some asymptotic formulae related to the Möbius function of higher order

Speaker：Biao Wang (Yunnan University)

Time：2026-6-19 15:00

Location：Conference Room S107 at Experiment Building at Haiyun Campus

Abstract:

In 1970, Apostol introduced the Möbius function of order k for an integer k ≥ 1. In 2001, it was generalized by Bege to the Möbius function μk,m of two parameters for any integers m ≥ k ≥ 1. In this article, we will establish three kinds of asymptotic formulae related to μk,m for m ≥ k ≥ 2 in a unified elementary method. These formulae 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.