Mean values of arithmetic functions and application to sums of powers

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

References in corpus (5)

• Nair-Tenenbaum bounds uniform with respect to the discriminant
• Sums of arithmetic functions over values of binary forms
• Representations of integers by systems of three quadratic forms
• An upper bound on the mean value of the Erdős-Hooley Delta function
• $6$-torsion and integral points on quartic threefolds