Mean values of arithmetic functions and application to sums of powers
Number Theory
2026-01-14 v6
Abstract
We provide new upper bounds for sums of certain arithmetic functions in many variables at polynomial arguments and, exploiting recent progress on the mean-value of the Erd\H os-Hooley -function, we derive lower bounds for the cardinality of those integers not exceeding a given limit that are expressible as some sums of powers.
Cite
@article{arxiv.2403.19320,
title = {Mean values of arithmetic functions and application to sums of powers},
author = {Régis de la Bretèche and Gérald Tenenbaum},
journal= {arXiv preprint arXiv:2403.19320},
year = {2026}
}