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DTSTART;TZID=America/Los_Angeles:20261118T161500
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SUMMARY:CCMS Colloquium: Non-Vanishing of L-Functions — Alexander Dunn (Georgia Institute of Technology)
DESCRIPTION:Abstract: Dirichlet’s 1837 proof of his theorem on primes in arithmetic progressions depended on the non-vanishing of \(L(1\,\chi)\) for nonprincipal characters. The Birch and Swinnerton-Dyer conjecture relates the rank of an elliptic curve to the order of vanishing of its \(L\)-function at the central point. Determining whether an individual central value vanishes can be difficult\, but averaging over families allows us to prove non-vanishing for many members at once. \nI will discuss this approach for cubic and quartic Hecke \(L\)-functions and the predictions from random matrix theory. Recent joint work establishes unconditionally that a positive proportion of the members of certain families have nonzero central values. In the quartic case\, our methods also show that a positive proportion of the curves \(y^2=x^3-qx\)\, with squarefree \(q\in\mathbb Z[i]\) ordered by norm\, have rank zero over \(\mathbb Q(i)\). \nThe cubic work is joint with Chantal David\, Alexandre de Faveri\, and Joshua Stucky. The quartic work is joint with Cruz Castillo and Alexandre de Faveri. \n\n\n\nFor questions about the event\, please contact your CCMS Colloquium chairs: \nProf. Robert Cass (Robert.Cass@ClaremontMcKenna.edu) or Prof. Qidi Peng (Qidi.Peng@cgu.edu) \nFor logistical questions\, contact Maxwell Kooiker (Maxwell.Kooiker@cgu.edu)\, the CCMS Colloquium Assistant.
URL:https://colleges.claremont.edu/ccms/event/ccms-colloquium-non-vanishing-of-l-functions-alexander-dunn-georgia-institute-of-technology/
LOCATION:Burkle 16\, Claremont Graduate University\, 1021 N. Dartmouth Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
ORGANIZER;CN="Qidi Peng":MAILTO:Qidi.Peng@cgu.edu
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