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SUMMARY:Aled Walker (King's College London)
DTSTART:20220504T150000Z
DTEND:20220504T160000Z
DTSTAMP:20260418T064005Z
UID:LNTS/68
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/68/">Co
 rrelations of sieve weights and distributions of zeros</a>\nby Aled Walker
  (King's College London) as part of London number theory seminar\n\nLectur
 e held in King's Building K0.18\, King's College London.\n\nAbstract\nIn t
 his talk we will discuss Montgomery's pair correlation conjecture for the 
 zeros of the Riemann zeta function. This is a deep spectral conjecture\, c
 losely related to several arithmetic conjectures on the distribution of pr
 imes. For example\, even assuming a strong form of the twin prime conjectu
 re\, one would only resolve Montgomery's conjecture in a limited range. Ye
 t\, building on work of Goldston and Gonek from the late 1990s\, we will p
 resent a recent conditional lower bound on the Fourier transform of Montgo
 mery's pair correlation function\, valid under milder hypotheses. The new 
 technical ingredient is a correlation estimate for the Selberg sieve weigh
 ts\, for which the level of support of the weights lies beyond the classic
 al square-root barrier.\n
LOCATION:https://researchseminars.org/talk/LNTS/68/
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