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

Part of: Multiplicative number theory

Published online by Cambridge University Press:  19 December 2025

Biao Wang Open the ORCID record for Biao Wang [Opens in a new window]
Biao Wang*
Affiliation:
School of Mathematics and Statistics, Yunnan University, Kunming, Yunnan, China (bwang@ynu.edu.cn)
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Abstract

Recently, Donoso, Le, Moreira, and Sun studied the asymptotic behaviour 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 the 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.

Keywords

completely multiplicative functionsGaussian integersprimitive lattice pointsWirsing’s theorem

MSC classification

Secondary: 11N99: None of the above, but in this section

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 14
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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