New findings reveal upper bounds for arithmetic functions and lower bounds for sums of powers, indicating potential applications.
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 Δ -function, we derive lower bounds for the cardinality of those integers not exceeding a given limit that are expressible as certain sums of powers.
No takes yet. Share an insight, caveat, or question.
Bretèche et al. (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: