Almost sure lower bounds for a model problem for multiplicative chaos in number theory. Issue 4 (10th October 2022)

• Record Type: Journal Article
• Authors: Gerspach, Maxim
• Is Part Of: Mathematika. Volume 68:Issue 4(2022)
• Page Start: 1331
• Page End: 1363
• Publication Date: 2022-10-10
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1112/mtk.12170
• Languages: English
• ISSNs: 0025-5793

Abstract

Abstract: The goal of this work is to prove an analogue of a recent result of Harper on almost sure lower bounds of random multiplicative functions, in a setting that can be thought of as a simplified function field analogue. It answers a question raised in the work of Soundararajan and Zaman, who proved moment bounds for the same quantity in analogy to those of Harper in the random multiplicative setting. Having a simpler quantity allows us to make the proof close to self‐contained, and perhaps somewhat more accessible.