Almost primes in almost all short intervals II

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dc.contributor.authorMatomäki Kaisa
dc.contributor.authorTeräväinen Joni
dc.contributor.organizationfi=matematiikka|en=Mathematics|
dc.contributor.organization-code1.2.246.10.2458963.20.41687507875
dc.converis.publication-id180246225
dc.converis.urlhttps://research.utu.fi/converis/portal/Publication/180246225
dc.date.accessioned2025-08-27T23:16:28Z
dc.date.available2025-08-27T23:16:28Z
dc.description.abstract<p>We show that, for almost all x, the interval (x, x + (log x)<sup>2.1</sup>] 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.</p>
dc.format.pagerange5433
dc.format.pagerange5459
dc.identifier.eissn1088-6850
dc.identifier.jour-issn0002-9947
dc.identifier.olddbid203715
dc.identifier.oldhandle10024/186742
dc.identifier.urihttps://www.utupub.fi/handle/11111/46086
dc.identifier.urlhttps://doi.org/10.1090/tran/8869
dc.identifier.urnURN:NBN:fi-fe2025082786177
dc.language.isoen
dc.okm.affiliatedauthorMatomäki, Kaisa
dc.okm.affiliatedauthorTeräväinen, Joni
dc.okm.discipline111 Mathematicsen_GB
dc.okm.discipline111 Matematiikkafi_FI
dc.okm.internationalcopublicationnot an international co-publication
dc.okm.internationalityInternational publication
dc.okm.typeA1 ScientificArticle
dc.publisherAMER MATHEMATICAL SOC
dc.publisher.countryUnited Statesen_GB
dc.publisher.countryYhdysvallat (USA)fi_FI
dc.publisher.country-codeUS
dc.relation.doi10.1090/tran/8869
dc.relation.ispartofjournalTransactions of the American Mathematical Society
dc.relation.issue8
dc.relation.volume376
dc.source.identifierhttps://www.utupub.fi/handle/10024/186742
dc.titleAlmost primes in almost all short intervals II
dc.year.issued2023

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