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).
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