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 Erdős—Hooley $\Delta$ -function, we derive lower bounds for the cardinality of those integers not exceeding a given limit that are expressible as certain sums of powers.
Authors
- Gérald Tenenbaum (ORCID: https://orcid.org/0000-0002-0478-3693)
- Régis de la Bretèche (ORCID: https://orcid.org/0000-0002-6713-9766)
Institutions
- Université Paris Cité (FR)
- Institut Élie Cartan de Lorraine (FR)
- Sorbonne Université (FR)
- Sorbonne Paris Cité (FR)
Publication Details
- Journal
- Mathematical Proceedings of the Cambridge Philosophical Society
- Published
- 2025-08-08
- DOI
- https://doi.org/10.1017/s0305004125101382
- Primary Topic
- Analytic Number Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 0.00