A1 Refereed original research article in a scientific journal

Almost primes in almost all short intervals II



Authors: Matomäki Kaisa, Teräväinen Joni

Publisher: AMER MATHEMATICAL SOC

Publication year: 2023

Journal: Transactions of the American Mathematical Society

Journal name in source: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

Journal acronym: T AM MATH SOC

Volume: 376

Issue: 8

First page : 5433

Last page: 5459

Number of pages: 27

ISSN: 0002-9947

eISSN: 1088-6850

DOI: https://doi.org/10.1090/tran/8869

Web address : https://doi.org/10.1090/tran/8869

Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/180246225


Abstract

We show that, for almost all x, the interval (x, x + (log x)2.1] contains products of exactly two primes. This improves on a work of the second author that had 3.51 in place of 2.1. To obtain this improvement, we prove a new type II estimate. One of the new innovations is to use Heath-Brown's mean value theorem for sparse Dirichlet polynomials.


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Last updated on 2024-26-11 at 13:59