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arXiv · 2406.09243

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

Biao Wang
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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.

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Biao Wang. 2025-12-16. On averages of completely multiplicative functions over co-prime integer pairs. https://doi.org/10.1017/prm.2025.10118

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