arXiv subjects
Publications and source records attributed to Xenia Dimitrakopoulou.
Let $Π$ be a regular algebraic cuspidal automorphic representation of $\mathrm{GL}_{3}(\mathbb{A}_{\mathbb{Q}})$ of weight $(a, 0, -a)$, and let $p$ be a prime. Generalising work of Loeffler--Williams in the nearly-ordinary case, we construct $p$-adic $L$-functions for each small slope regular $P_{1}$-refinement of $Π$ at $p$ consistent with the conjectures of Coates--Perrin-Riou and Panchishkin.
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.