p-adic L-functions 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.

152 pages. Accepted for publication in Forum of Mathematics, Pi

References in corpus (4)

• Endoscopic Classification of Representations: Inner Forms of Unitary Groups
• p-adic q-expansion principles on unitary Shimura varieties
• Differential operators, pullbacks, and families of automorphic forms
• A p-adic Eisenstein measure for vector-weight automorphic forms

Cited by in corpus (7)

• A p-adic Eisenstein measure for vector-weight automorphic forms
• Archimedean Zeta Integrals for Unitary Groups
• An introduction to Eisenstein measures
• An introduction to $p$-adic $L$-functions
• Automorphic Forms on Unitary Groups
• Square root $p$-adic $L$-functions, I: Construction of a one-variable measure
• Theta cycles and the Beilinson--Bloch--Kato conjectures