Back to Search
Start Over
Multiplicative recurrence of M\'obius transformations
- Publication Year :
- 2024
-
Abstract
- We provide a necessary and sufficient condition under which the set defined by a M\"obius transformation of positive integers is a set of multiplicative recurrence. A Khinchin-type lower bound is also established. This not only answers a question of Donoso--Le--Moreira--Sun but also strengthens their result. The key input in our proof is Tao's logarithmically averaged correlations of non-pretentious multiplicative functions.<br />Comment: In Lemma 4.1, [FH16, Theorem 1.4] is not applicable. In Lemma 6.2, it is not necessarily true that max{k:a^k|r} = max{k:a^k|s}
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2409.12936
- Document Type :
- Working Paper