On averages of completely multiplicative functions over co-prime integer pairs

Abstract

Recently, Donoso, Le, Moreira and Sun studied the asymptotic behavior of the averages of completely multiplicative functions over the Gaussian integers. They derived Wirsing's theorem for Gaussian integers, answered a question of Frantzikinakis and Host for sum of two squares, and obtained a variant of a theorem of Bergelson and Richter on ergodic averages along the number of prime factors of integers. In this paper, we will show the analogue of these results for co-prime integer pairs. Moreover, building on Frantzikinakis and Host's results, we obtain some convergences on the multilinear averages of multiplicative functions over primitive lattice points.

arXiv comment12 pages

References in corpus (5)

• Asymptotics for multilinear averages of multiplicative functions
• Linear correlations of multiplicative functions
• Dynamical generalizations of the Prime Number Theorem and disjointness of additive and multiplicative semigroup actions
• Dynamics on the number of prime divisors for additive arithmetic semigroups
• Generalizations of the Erdős-Kac Theorem and the Prime Number Theorem