BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:One-Level density for cubic characters over the Eisenstein field
DTSTART;VALUE=DATE-TIME:20210602T013000Z
DTEND;VALUE=DATE-TIME:20210602T024500Z
DTSTAMP;VALUE=DATE-TIME:20230325T181223Z
UID:indico-contribution-5723@indico.ipmu.jp
DESCRIPTION:Speakers: Chantal David (Concordia U.)\nKatz and Sarnak conjec
tured that statistics on zeroes of a family of L-functions on the critical
line should match statistics on eigenvalues of characteristic polynomials
of a group of random matrices\, where the group is chosen according to th
e properties of the family. For example\, the family of L-functions attach
ed to quadratic Dirichlet characters corresponds to symplectic matrices\,
and evidence for the conjecture of Katz and Sarnak was obtained by provin
g that the one-level density of zeroes of quadratic Dirichlet L-functions
matches the one-level density for eigenvalues of characteristic polynomial
s of symplectic matrices\,\nfor special test functions (with limited suppo
rt of the Fourier transform) by Ozluk and Snyder in 1999. Since the suppo
rt of the Fourier transform of the test function is large enough\, they ca
n deduce that more than $93.75 \\%$ of the L-functions attached to quadrat
ic Dirichlet characters are such that $L(1/2\, \\chi) \\neq 0$\, giving ev
idence for a well-known conjecture of Chowla. The full conjecture of Katz-
Sarnak\n(without any restrictions on the support of the Fourier transform)
implies that $100 \\%$ of the L-functions attached to quadratic Dirichlet
characters are such that $L(1/2\, \\chi) \\neq 0$.\n\nWe will review thos
e results and consider the case of L-functions attached to cubic Dirichle
t characters. We prove the first result towards the Katz and Sarnak conjec
ture for test functions with support of the Fourier transform large enough
to obtain a positive proportion of L-functions attached to cubic Dirichl
et characters such that $L(1/2\, \\chi) \\neq 0$.\n\nJoint work with Ahmet
M. Guloglu.\n\nhttps://indico.ipmu.jp/event/387/contributions/5723/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5723/
END:VEVENT
END:VCALENDAR