$p$-ADIC $L$-FUNCTIONS FOR UNITARY GROUPS. (6th May 2020)

• Record Type: Journal Article
• Authors: EISCHEN, ELLEN; HARRIS, MICHAEL; LI, JIANSHU; SKINNER, CHRISTOPHER
• Is Part Of: Forum of mathematics. Volume 8(2020)
• Publication Date: 2020-05-06
• Subjects: 11F85, -- 11F66, -- 14G10, -- 11F55, -- 11R23, -- 14G35, -- 11G10, -- 11F03; Mathematics -- Periodicals; 510
• DOI: 10.1017/fmp.2020.4
• Languages: English
• ISSNs: 2050-5086

Abstract

Abstract : This paper completes the construction of $p$ -adic $L$ -functions for unitary groups. More precisely, in Harris, Li and Skinner [' $p$ -adic $L$ -functions for unitary Shimura varieties. I. Construction of the Eisenstein measure', Doc. Math. Extra Vol. (2006), 393–464 (electronic)], three of the 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 [Eischen, 'A $p$ -adic Eisenstein measure for unitary groups', J. Reine Angew. Math. 699 (2015), 111–142; ' $p$ -adic differential operators on automorphic forms on unitary groups', Ann. Inst. Fourier (Grenoble) 62 (1) (2012), 177–243], Part II of the present paper provides the calculations of local $\unicode[STIX]{x1D701}$ -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.