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

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• Xenia Dimitrakopoulou (Warwick)
• Tuesday 30 April 2024, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Jef Laga.

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.

This talk is part of the Number Theory Seminar series.

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