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