A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Almost primes in almost all very short intervals
Tekijät: Matomäki Kaisa
Kustantaja: WILEY
Julkaisuvuosi: 2022
Journal: Journal of the London Mathematical Society
Tietokannassa oleva lehden nimi: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
Lehden akronyymi: J LOND MATH SOC
Sivujen määrä: 37
ISSN: 0024-6107
eISSN: 1469-7750
DOI: https://doi.org/10.1112/jlms.12592
Verkko-osoite: https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.12592
Rinnakkaistallenteen osoite: 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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