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SUMMARY:The exceptional zero conjecture for GL(3) - Andrew Graham (Oxford)
DTSTART:20250218T143000Z
DTEND:20250218T153000Z
UID:TALK225658@talks.cam.ac.uk
CONTACT:Rong Zhou
DESCRIPTION:If E is an elliptic curve over Q with split multiplicative red
 uction at p\, then the p-adic L-function associated with E vanishes at s=1
  independently of whether the complex L-function vanishes. In this case\, 
 one has an "exceptional zero formula" relating the first derivative of the
  p-adic L-function to the complex L-function multiplied by a certain L-inv
 ariant. This L-invariant can be interpreted in several ways -- on the auto
 morphic side for example\, L-invariants parameterise part of the p-adic lo
 cal Langlands correspondence for GL(2)(Q_p).\n\nIn this talk\, I will disc
 uss an exceptional zero formula for (not necessarily essentially self-dual
 ) regular algebraic\, cuspidal automorphic representations of GL(3) which 
 are Steinberg at p. The formula involves an automorphic L-invariant constr
 ucted by Gehrmann. Joint work with Daniel Barrera and Chris Williams.
LOCATION:MR13
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