p-adic L-functions for unitary groups

TL;DR

This paper completes the construction of p-adic L-functions for unitary groups by building on previous approaches, involving local integral calculations and formalism for pairing Eisenstein measures with Hida families.

Contribution

It finalizes the construction of p-adic L-functions for unitary groups by integrating recent advances in Eisenstein measures, p-adic differential operators, and the doubling method.

Findings

Calculation of local ζ-integrals at p and other places

Development of formalism for pairing Eisenstein measures with Hida families

Completion of the p-adic L-function construction for unitary groups

Abstract

This paper completes the construction of $p$-adic $L$-functions for unitary groups. More precisely, in 2006, the last three named authors proposed an approach to constructing such $p$-adic $L$-functions (Part I). Building on more recent results, including the first named author's construction of Eisenstein measures and $p$-adic differential operators, Part II of the present paper provides the calculations of local $\zeta$-integrals occurring in the Euler product (including at $p$). Part III of the present paper develops the formalism needed to pair Eisenstein measures with Hida families in the setting of the doubling method.