Vol. 14, No. 1, 2020

Download this article
Download this article For screen
For printing
Recent Issues

Volume 14
Issue 10, 2575–2813
Issue 9, 2295–2574
Issue 8, 2001–2294
Issue 7, 1669–1999
Issue 6, 1331–1667
Issue 5, 1055–1329
Issue 4, 815–1054
Issue 3, 545–813
Issue 2, 275–544
Issue 1, 1–274

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
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 : 𝕋, where 𝕋 denotes the unit circle, such that

{(f(n),g(n + 1))}n1¯𝕋 × 𝕋.

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

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