$p$-ADIC EISENSTEIN SERIES AND $L$-FUNCTIONS OF CERTAIN CUSP FORMS ON DEFINITE UNITARY GROUPS. (21st November 2014)

• Record Type: Journal Article
• Authors: Eischen, Ellen; Wan, Xin
• Is Part Of: Journal of the Institute of Mathematics of Jussieu. Volume 15:Number 3(2016:Jul.)
• Page Start: 471
• Page End: 510
• Publication Date: 2014-11-21
• Subjects: Primary 11F33, -- 11F03, -- Secondary 11F30, -- 11S40, -- 11G18, -- 11F55, -- 11F85; p-adic automorphic forms, -- automorphic forms on unitary groups, -- Eisenstein series, -- p-adic L-functions, -- Klingen–Eisenstein series; Mathematics -- Periodicals; 510.5
• DOI: 10.1017/S1474748014000395
• Languages: English
• ISSNs: 1474-7480

Abstract

Abstract : We construct $p$ -adic families of Klingen–Eisenstein series and $L$ -functions for cusp forms (not necessarily ordinary) unramified at an odd prime $p$ on definite unitary groups of signature $(r, 0)$ (for any positive integer $r$ ) for a quadratic imaginary field ${\mathcal{K}}$ split at $p$ . When $r=2$, we show that the constant term of the Klingen–Eisenstein family is divisible by a certain $p$ -adic $L$ -function.