Multiplicative recurrence of Möbius transformations

Abstract

We establish a complete characterization of multiplicative recurrence for images of the positive integers under Möbius transformations, answering a question of Donoso--Le--Moreira--Sun in the negative. As a consequence, we strengthen and extend a Diophantine approximation result of Charamaras--Mountakis--Tsinas, confirming their conjectures.

13 pages. We answer a question of Donoso--Le--Moreira--Sun in the negative, correcting our earlier claim