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$p$ -ADIC EISENSTEIN SERIES AND $L$ -FUNCTIONS OF CERTAIN CUSP FORMS ON DEFINITE UNITARY GROUPS

  • Ellen Eischen (a1) and Xin Wan (a2)

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.

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$p$ -ADIC EISENSTEIN SERIES AND $L$ -FUNCTIONS OF CERTAIN CUSP FORMS ON DEFINITE UNITARY GROUPS

  • Ellen Eischen (a1) and Xin Wan (a2)

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