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PRODID:-//Columba Systems Ltd//NONSGML CPNG/SpringViewer/ICal Output/3.3-
M3//EN
VERSION:2.0
CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20220421T104553Z
DTSTART:20220503T140000Z
DTEND:20220503T150000Z
SUMMARY:Jared Lichtman (Oxford) - Twin primes & a modified linear sieve
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}q149-kz1ed1
9l-1ibha
DESCRIPTION:Abstract : The linear sieve is a powerful tool to tackle prob
lems related to the primes\, when combined with equidistribution estimat
es for the remainder. In 1977 Iwaniec introduced a well-factorable modif
ication of the linear sieve to prove there are infinitely many integers
n such that n^2+1 has at most two prime factors. Furthermore\, the (well
-factorable) linear sieve leads to the best known upper bounds for twin
primes. These bounds use work of Bombieri\, Friedlander\, and Iwaniec fr
om 1986\, showing these sieve weights equidistribute primes of size x in
arithmetic progressions to moduli up to x^{4/7}. This level was recentl
y increased to x^{7/12} by Maynard. We introduce a new modification of t
he linear sieve whose weights equidistribute primes of size x to level x
^{10/17}. As an application we refine a 2004 upper bound for twin primes
of Wu\, which gives the largest percent improvement since the work of B
ombieri\, Friedlander\, and Iwaniec.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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