English

Two arithmetic applications of perturbations of composition operators

Number Theory 2020-02-27 v1 Dynamical Systems

Abstract

We estimate the spectral radius of perturbations of a particular family of composition operators, in a setting where the usual choices of norms do not account for the typical size of the perturbation. We apply this to estimate the growth rate of large moments of a Thue-Morse generating function and of the Stern sequence. This answers in particular a question of Mauduit, Montgomery and Rivat (2018).

Keywords

Cite

@article{arxiv.2002.11417,
  title  = {Two arithmetic applications of perturbations of composition operators},
  author = {Sandro Bettin and Sary Drappeau},
  journal= {arXiv preprint arXiv:2002.11417},
  year   = {2020}
}

Comments

11 pages

R2 v1 2026-06-23T13:54:23.638Z