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SUMMARY:Chantal David
DTSTART:20201026T160000Z
DTEND:20201026T170000Z
DTSTAMP:20260423T053133Z
UID:UNYONTC/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UNYONTC/11/"
 >Moments and non-vanishing of cubic Dirichlet L-functions at s=1/2</a>\nby
  Chantal David as part of Upstate New York Online Number Theory Colloquium
 \n\n\nAbstract\nA famous conjecture of Chowla predicts that $L(\\frac{1}{2
 }\,\\chi)\\neq 0$  for all Dirichlet L-functions\nattached to primitive ch
 aracters $\\chi$. It was conjectured first in the case where $\\chi$ is a 
 quadratic\ncharacter\, which is the most studied case. For quadratic Diric
 hlet L-functions\, Soundararajan\nproved that at least 87.5% of the quadra
 tic Dirichlet L-functions do not vanish at $s=\\frac{1}{2}.$\n\nUnder GRH\
 , there are slightly stronger results by Ozlek and Snyder.\nWe present in 
 this talk the first result showing a positive proportion of cubic Dirichle
 t\nL-functions non-vanishing at s = 1/2 for the non-Kummer case over funct
 ion fields. This\ncan be achieved by using the recent breakthrough work on
  sharp upper bounds for moments\nof Soundararajan\, Harper and Lester-Radz
 iwill. Our results would transfer over number\nfields (but we would need t
 o assume GRH in this case).\nThe talk will be accessible to a general audi
 ence of number theorists and graduate students\nin number theory.\n\nJoint
  work with A. Florea and M. Lalin.\n
LOCATION:https://researchseminars.org/talk/UNYONTC/11/
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