An explicit result for short sums of positive arithmetic functions

Olivier Bordellès

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arXiv · 2402.12333

An explicit result for short sums of positive arithmetic functions

Olivier Bordellès

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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 $\Delta$-function in short intervals.

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Olivier Bordellès. 2024-02-19. An explicit result for short sums of positive arithmetic functions. https://arxiv.org/abs/2402.12333

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