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SUMMARY:Natalie Evans
DTSTART:20210630T150000Z
DTEND:20210630T160000Z
DTSTAMP:20260418T064941Z
UID:LNTS/45
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/45/">Co
 rrelations of almost primes</a>\nby Natalie Evans as part of London number
  theory seminar\n\n\nAbstract\nThe Hardy-Littlewood generalised twin prime
  conjecture states an asymptotic formula for the number of primes $p\\le X
 $ such that $p+h$ is prime for any non-zero even integer $h$. While this c
 onjecture remains wide open\, Matomaki\, Radziwill and Tao proved that it 
 holds on average over $h$\, improving on a previous result of Mikawa. In t
 his talk we will discuss an almost prime analogue of the Hardy-Littlewood 
 conjecture for which we can go beyond what is known for primes. We will de
 scribe some recent work in which we prove an asymptotic formula for the nu
 mber of almost primes $n=p_1p_2 \\le X$ such that $n+h$ has exactly two pr
 ime factors which holds for a very short average over $h$.\n
LOCATION:https://researchseminars.org/talk/LNTS/45/
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