BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Sacha Mangerel (Durham University)
DTSTART:20260325T160000Z
DTEND:20260325T170000Z
DTSTAMP:20260528T081214Z
UID:LNTS/191
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/191/">A
 nalogues of the binary Goldbach problem for integers with an odd number of
  prime factors</a>\nby Sacha Mangerel (Durham University) as part of Londo
 n number theory seminar\n\nLecture held in University College London\, Roo
 m 505.\n\nAbstract\nThe binary Goldbach problem\, which asserts that every
  large enough even integer is a sum of two primes\, is known to be intract
 able via sieve methods alone\, due to the ``parity problem''. A few years 
 ago\, Shusterman asked the following relaxation of binary Goldbach that ne
 vertheless suffers from the same parity obstruction: can every large enoug
 h even integer be expressible as a sum of two integers\, both with an odd 
 number of prime factors?\n\nIn this talk I will discuss this and other rel
 ated problems. In particular\, I will explain my recent solution to Shuste
 rman's problem\, conditional on the GRH for Dirichlet L-functions (or inde
 ed\, something much weaker).  The proof involves a careful study of symmet
 ries of exponential sums involving the Liouville function that encode comb
 inatorial data\, linked together\, somewhat surprisingly\, by an algorithm
  of Pierce towards expressing rational numbers as an alternating series of
  a given type.\n
LOCATION:https://researchseminars.org/talk/LNTS/191/
END:VEVENT
END:VCALENDAR