On the orbits of multiplicative pairs

Klurman, Oleksiy; Mangerel, Alexander P.

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.

Citation

Klurman, O., & Mangerel, A. P. (2020). On the orbits of multiplicative pairs. Algebra & Number Theory, 14(1), 155–189. https://doi.org/10.2140/ant.2020.14.155

• Journal Article Type: Article
• Acceptance Date: Aug 5, 2019
• Publication Date: Mar 15, 2020
• Deposit Date: Oct 20, 2021
• Journal: Algebra & Number Theory
• Print ISSN: 1937-0652
• Electronic ISSN: 1944-7833
• Publisher: Mathematical Sciences Publishers (MSP)
• Volume: 14
• Issue: 1
• Pages: 155–189
• DOI: https://doi.org/10.2140/ant.2020.14.155
• Public URL: https://durham-repository.worktribe.com/output/1233925