The Differences Between Consecutive Primes, V

DOI10.1093/IMRN/RNZ295zbMATH Open1492.11136arXiv1906.09555OpenAlexW3111825584MaRDI QIDQ5022041

D. R. Heath-Brown

Publication date: 18 January 2022

Published in: IMRN. International Mathematics Research Notices (Search for Journal in Brave)

Abstract: We show that [sum_{substack{p_nle x\ p_{n+1}-p_ngesqrt{p_n}}}(p_{n+1}-p_n)ll_{varepsilon} x^{3/5+varepsilon}] for any fixed $varepsilon>0$. This improves a result of Matom"{a}ki, in which the exponent was $2/3$.

Full work available at URL: https://arxiv.org/abs/1906.09555

zbMATH Keywords

differences between consecutive primesmean values of Dirichlet polynomials

Mathematics Subject Classification ID

Distribution of primes (11N05)

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