On completely multiplicative ± 1 sequences that omit many consecutive + 1 values

You, Yichen

Abstract

We say that ±1-valued completely multiplicative functions are length-𝑘 functions 𝑓 if they take the value +1 at at most 𝑘 consecutive integers. We introduce a method to extend the length of 𝑓 using the idea of the “rotation trick” in [7]. Under the assumption of Elliott’s conjecture, this method allows us to construct length-𝑘 functions systematically for 𝑘 ⩾ 4 which generalizes the work of Schur for 𝑘=2 and Hudson for 𝑘=3.

Citation

You, Y. (2025). On completely multiplicative ± 1 sequences that omit many consecutive + 1 values. Bulletin of the London Mathematical Society, 57(6), 1708-1717. https://doi.org/10.1112/blms.70056

• Journal Article Type: Article
• Acceptance Date: Mar 3, 2025
• Online Publication Date: Mar 31, 2025
• Publication Date: 2025-06
• Deposit Date: Apr 17, 2025
• Publicly Available Date: Apr 17, 2025
• Journal: Bulletin of the London Mathematical Society
• Print ISSN: 0024-6093
• Electronic ISSN: 1469-2120
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 57
• Issue: 6
• Pages: 1708-1717
• DOI: https://doi.org/10.1112/blms.70056
• Public URL: https://durham-repository.worktribe.com/output/3781045