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SUMMARY:Anticyclotomic $p$-adic $L$-functions for families of $U_n \\times
  U_{n+1}$ - Xenia Dimitrakopoulou (Warwick)
DTSTART:20240430T133000Z
DTEND:20240430T143000Z
UID:TALK215623@talks.cam.ac.uk
CONTACT:Jef Laga
DESCRIPTION:I will report on recent work on the construction of anticyclot
 omic $p$-adic $L$-functions for Rankin--Selberg products. I will explain h
 ow by $p$-adically interpolating the branching law for the spherical pair 
 $\\left(U_n\, U_n \\times U_{n+1}\\right)\,$ we can construct a $p$-adic $
 L$-function attached to cohomological automorphic representations of $U_n 
 \\times U_{n+1}$. Due to the recent proof of the unitary Gan--Gross--Prasa
 d conjecture\, this $p$-adic $L$-function interpolates the square root of 
 all critical $L$-values\, including anticyclotomic variation. Time allowin
 g\, I will explain how we can extend this result to the Coleman family of 
 an automorphic representation.
LOCATION:MR13
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