Oleksiy Klurman
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 |
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