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arXiv · 2410.02480

R\'epartition conjointe de trois nombres premiers et applications

Régis de la Bretèche
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Abstract

We prove asymptotic results for the singular series associated to the distribution of three primes. Assuming a quantitative version of Hardy and Littlewood's conjecture on prime 3-tuples, we deduce an asymptotic formula related to the joint distribution of three primes. This improves recent results of Kuperberg and completes results by Montgomery and Soundararajan. Following the Montgomery and Soundararajan approach, we derive conjectural applications to the distribution of primes in short intervals.

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Régis de la Bretèche. 2024-10-03. R\'epartition conjointe de trois nombres premiers et applications. https://arxiv.org/abs/2410.02480

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