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2020 On the orbits of multiplicative pairs
Oleksiy Klurman, Alexander P. Mangerel
Algebra Number Theory 14(1): 155-189 (2020). DOI: 10.2140/ant.2020.14.155

Abstract

We characterize all pairs of completely multiplicative functions f g : 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

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Oleksiy Klurman. Alexander P. Mangerel. "On the orbits of multiplicative pairs." Algebra Number Theory 14 (1) 155 - 189, 2020. https://doi.org/10.2140/ant.2020.14.155

Information

Received: 24 January 2019; Revised: 3 July 2019; Accepted: 5 August 2019; Published: 2020
First available in Project Euclid: 7 April 2020

zbMATH: 07180784
MathSciNet: MR4076810
Digital Object Identifier: 10.2140/ant.2020.14.155

Subjects:
Primary: 11N37
Secondary: 11N64

Rights: Copyright © 2020 Mathematical Sciences Publishers

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