Regularity properties of $k$-Brjuno and Wilton functions
Dynamical Systems
2024-03-20 v2 Number Theory
Abstract
We study functions related to the classical Brjuno function, namely -Brjuno functions and the Wilton function. Both appear in the study of boundary regularity properties of (quasi) modular forms and their integrals. We consider various possible versions of them, based on the -continued fraction developments. We study their BMO regularity properties and their behaviour near rational numbers of their finite truncations.
Keywords
Cite
@article{arxiv.2106.07298,
title = {Regularity properties of $k$-Brjuno and Wilton functions},
author = {Seul Bee Lee and Stefano Marmi and Izabela Petrykiewicz and Tanja I. Schindler},
journal= {arXiv preprint arXiv:2106.07298},
year = {2024}
}
Comments
64 pages, comments welcome