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SUMMARY:Chantal David (Concordia University)
DTSTART:20201216T160000Z
DTEND:20201216T170000Z
DTSTAMP:20260423T024741Z
UID:hnts/18
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/hnts/18/">Mo
 ments and non-vanishing of cubic Dirichlet $L$-functions at $s =\\frac{1}{
 2}$</a>\nby Chantal David (Concordia University) as part of Heilbronn numb
 er theory seminar\n\n\nAbstract\nA famous conjecture of Chowla predicts th
 at $L(\\frac{1}{2}\,\\chi) \\neq 0$ for all Dirichlet $L$-functions attach
 ed to primitive characters $\\chi$. It was conjectured first in the case w
 here $\\chi$ is a quadratic character\, which is the most studied case. Fo
 r quadratic Dirichlet $L$-functions\, Soundararajan proved that at least 8
 7.5% of the quadratic Dirichlet L-functions do not vanish at $s =\\frac{1}
 {2}$. Under GRH\, there are slightly stronger results by Ozlek and Snyder.
 \n\nWe present in this talk the first result showing a positive proportion
  of cubic Dirichlet\n$L$-functions non-vanishing at $s =\\frac{1}{2}$ for 
 the non-Kummer case over function fields. This can be achieved by using th
 e recent breakthrough work on sharp upper bounds for moments of\nSoundarar
 ajan\, Harper and Lester-Radziwill. Our results would transfer over number
  fields\,\nbut we would need to assume GRH in this case.\n
LOCATION:https://researchseminars.org/talk/hnts/18/
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