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arXiv · 2312.05841

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

Xenia Dimitrakopoulou
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Abstract

By $p$-adically interpolating the branching law for the spherical pair $\left(U_n, U_{n+1} \times U_{n}\right)$ of definite unitary groups, we construct a $p$-adic $L$-function attached to cohomological automorphic representations of $U_{n+1} \times U_{n}$. Under a further multiplicity one assumption, we extend the construction to Coleman families. Our $p$-adic $L$-function interpolates the square root of the central critical $L$-value. It has weight and anticyclotomic variables and its construction relies on the proof of the unitary Gan--Gross--Prasad conjecture.

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Xenia Dimitrakopoulou. 2023-12-10. Anticyclotomic $p$-adic $L$-functions for Coleman families of $U_{n+1} \times U_{n}$. https://arxiv.org/abs/2312.05841

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