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An explicit result for short sums of positive arithmetic functions

Number Theory 2025-01-07 v3

Abstract

We prove a totally explicit bound for short sums of certain non-negative arithmetic functions satisfying a general growth condition, and apply this result to derive two explicit estimates for the Erd\H{o}s-Hooley Δ\Delta-function in short intervals.

Keywords

Cite

@article{arxiv.2402.12333,
  title  = {An explicit result for short sums of positive arithmetic functions},
  author = {Olivier Bordellès},
  journal= {arXiv preprint arXiv:2402.12333},
  year   = {2025}
}

Comments

23 pages; comments are welcome