Anticyclotomic $p$-adic $L$-functions for families of $U_n \times U_{n+1}$

Xenia Dimitrakopoulou

Date(s) : 20/02/2024   iCal
14 h 00 min - 15 h 00 min

I will report on recent work on the construction of anticyclotomic $p$-adic $L$-functions for Rankin–Selberg products. I will explain how 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–Prasad conjecture, this $p$-adic $L$-function interpolates the square root of all critical $L$-values, including anticyclotomic variation. Time allowing, I will explain how we can extend this result to the Coleman family of an automorphic representation.

Site Sud, Luminy, TPR2, Salle de Séminaire 304-306 (3ème étage)


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