Ergodic averages with the Hecke eigenvalue square weights and the Piltz divisor function weights
Dynamical Systems
2023-10-18 v4 Number Theory
Abstract
In this paper, we prove that the Hecke eigenvalue square for a holomorphic cusp form and the Piltz divisor functions are good weighting functions for the pointwise ergodic theorem. This partially solves problems suggested by Cuny and Weber. Additionally, we prove similar results for various other arithmetical functions in the last section.
Keywords
Cite
@article{arxiv.2211.11552,
title = {Ergodic averages with the Hecke eigenvalue square weights and the Piltz divisor function weights},
author = {Jiseong Kim},
journal= {arXiv preprint arXiv:2211.11552},
year = {2023}
}
Comments
15 pages. To appear JMAA