BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Chris Williams (University of Warwick)
DTSTART:20211110T150000Z
DTEND:20211110T160000Z
DTSTAMP:20260418T064328Z
UID:LNTS/52
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/52/">$p
 $-adic $L$-functions for GL(3)</a>\nby Chris Williams (University of Warwi
 ck) as part of London number theory seminar\n\nLecture held in Huxley 144\
 , Imperial.\n\nAbstract\nLet $\\pi$ be a $p$-ordinary cohomological cuspid
 al automorphic representation of $GL_n(\\mathbb{A}_\\mathbb{Q})$. A conjec
 ture of Coates--Perrin-Riou predicts that the (twisted) critical values of
  its $L$-function $L(\\pi \\times \\chi\,s)$\, for Dirichlet characters $\
 \chi$ of $p$-power conductor\, satisfy systematic congruence properties mo
 dulo powers of $p$\, captured in the existence of a $p$-adic $L$-function.
  For $n = 1\,2$ this conjecture has been known for decades\, but for $n \\
 geq 3$ it is known only in special cases\, e.g. symmetric squares of modul
 ar forms\; and in all known cases\, $\\pi$ is a functorial transfer from a
  proper subgroup of $GL_n$. I will explain what a $p$-adic $L$-function is
 \, state the conjecture more precisely\, and then report on ongoing joint 
 work with David Loeffler\, in which we prove this conjecture for $n=3$ (wi
 thout any transfer or self-duality assumptions).\n
LOCATION:https://researchseminars.org/talk/LNTS/52/
END:VEVENT
END:VCALENDAR