BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Andrew Graham (University of Oxford)
DTSTART:20250205T160000Z
DTEND:20250205T170000Z
DTSTAMP:20260418T065701Z
UID:LNTS/156
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/156/">T
 he exceptional zero conjecture for $\\mathrm{GL}(3)$</a>\nby Andrew Graham
  (University of Oxford) as part of London number theory seminar\n\nLecture
  held in Room 505\, Department of Mathematics (25 Gordon St)\, University 
 College London.\n\nAbstract\nIf $E$ is an elliptic curve over $\\mathbb{Q}
 $ with split multiplicative reduction at $p$\, then the $p$-adic $L$-funct
 ion associated with $E$ vanishes at $s=1$ independently of whether the com
 plex $L$-function vanishes. In this case\, one has an "exceptional zero fo
 rmula" relating the first derivative of the $p$-adic $L$-function to the c
 omplex $L$-function multiplied by a certain L-invariant. This L-invariant 
 can be interpreted in several ways -- on the automorphic side for example\
 , L-invariants parameterise part of the $p$-adic local Langlands correspon
 dence for $\\mathrm{GL}_2(\\mathbb{Q}_p)$.\n\nIn this talk\, I will discus
 s an exceptional zero formula for (not necessarily essentially self-dual) 
 regular algebraic\, cuspidal automorphic representations of $\\mathrm{GL}_
 3$ which are Steinberg at $p$. The formula involves an automorphic L-invar
 iant constructed by Gehrmann. Joint work with Daniel Barrera and Chris Wil
 liams.\n
LOCATION:https://researchseminars.org/talk/LNTS/156/
END:VEVENT
END:VCALENDAR