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SUMMARY:Daniel Fiorilli (Université Paris-Sud)
DTSTART:20210208T160000Z
DTEND:20210208T164500Z
DTSTAMP:20260423T022809Z
UID:IML_NT/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IML_NT/4/">H
 igher moments of primes in intervals and in arithmetic progressions\, I</a
 >\nby Daniel Fiorilli (Université Paris-Sud) as part of IML Number Theory
  semester (spring 2021)\n\n\nAbstract\nSince the work of Selberg and of Ba
 rban\, Davenport and Halberstam\, the variances of primes in intervals and
  in arithmetic progressions have been widely studied and continue to be an
  active topic of research. However\, much less is known about higher momen
 ts. Hooley established a bound on the third moment in progressions\, which
  was later sharpened by Vaughan for a variant involving a major arcs appro
 ximation. Little is known for moments of order four or higher\, other than
  the conjecture of Hooley and the conditional result of Montgomery-Soundar
 arajan. In this talk I will discuss recent joint work with Régis de la Br
 etèche on weighted moments in intervals and on weighted moments of moment
 s in progressions. In particular we will show how to deduce sharp uncondit
 ional omega results on all weighted even moments in certain ranges.\n
LOCATION:https://researchseminars.org/talk/IML_NT/4/
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