English

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 kk-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 α\alpha-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