Mean values of arithmetic functions and application to sums of powers

Régis de la Bretèche, Gérald Tenenbaum

Published 2024-03-28Version 1

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 $\Delta$-function, we derive lower bounds for the cardinality of those integers not exceeding a given limit that are expressible as some sums of powers.