A1 Refereed original research article in a scientific journal
Almost primes in almost all very short intervals
Authors: Matomäki Kaisa
Publisher: WILEY
Publication year: 2022
Journal: Journal of the London Mathematical Society
Journal name in source: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
Journal acronym: J LOND MATH SOC
Number of pages: 37
ISSN: 0024-6107
eISSN: 1469-7750
DOI: https://doi.org/10.1112/jlms.12592
Web address : https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.12592
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/175009419
We show that as soon as h ->infinity$h\rightarrow \infty$ with X ->infinity$X \rightarrow \infty$, almost all intervals (x-hlogX,x]$(x-h\log X, x]$ with x is an element of(X/2,X]$x \in (X/2, X]$ contain a product of at most two primes. In the proof we use Richert's weighted sieve, with the arithmetic information eventually coming from results of Deshouillers and Iwaniec on averages of Kloosterman sums.
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