Vol. 14, No. 1, 2020
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On the orbits of multiplicative pairs

Oleksiy Klurman and Alexander P. Mangerel
Vol. 14 (2020), No. 1, 155–189
DOI: 10.2140/ant.2020.14.155
Abstract

We characterize all pairs of completely multiplicative functions fg : ℕ → 𝕋, where 𝕋 denotes the unit circle, such that

{(f(n),g(n + 1))}n≥1¯≠𝕋 × 𝕋.

In so doing, we settle an old conjecture of Zoltán Daróczy and Imre Kátai.

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Keywords
multiplicative functions, Erdos discrepancy problem, Katai conjecture
Mathematical Subject Classification 2010
Primary: 11N37
Secondary: 11N64
Milestones
Received: 24 January 2019
Revised: 3 July 2019
Accepted: 5 August 2019
Published: 15 March 2020
Authors
Oleksiy Klurman
Department of Mathematics
Royal Institute of Technology
Stockholm
Sweden
Alexander P. Mangerel
Centre Recherches Mathematiques
Université de Montréal
Canada