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SUMMARY:Julia Stadlmann (University of Oxford)
DTSTART:20230503T150000Z
DTEND:20230503T160000Z
DTSTAMP:20260418T070221Z
UID:LNTS/97
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/97/">Th
 e mean square gap between primes</a>\nby Julia Stadlmann (University of Ox
 ford) as part of London number theory seminar\n\nLecture held in KCL\, Str
 and Building\, Room S3.30.\n\nAbstract\nConditional on the Riemann hypothe
 sis\, Selberg showed in 1943 that the average size of the squares of diffe
 rences between consecutive primes less than $x$ is $O(log(x)^4)$. Uncondit
 ional results still fall far short of this conjectured bound: Peck gave a 
 bound of $O(x^{0.25+\\epsilon})$ in 1996 and to date this is the best know
 n bound obtained using only methods from classical analytic number theory.
 \n\n\nIn this talk we discuss how sieve theory (in the form of Harman's si
 eve) can be combined with classical methods to improve bounds on the numbe
 r of short intervals which contain no primes\, thus improving the uncondit
 ional bound on the mean square gap between primes to $O(x^{0.23+\\epsilon}
 )$.\n
LOCATION:https://researchseminars.org/talk/LNTS/97/
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