Vol. 8, No. 10, 2014

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A $p$-adic Eisenstein measure for vector-weight automorphic forms

Ellen Eischen

Vol. 8 (2014), No. 10, 2433–2469
Abstract

We construct a $p$-adic Eisenstein measure with values in the space of vector-weight $p$-adic automorphic forms on certain unitary groups. This measure allows us to $p$-adically interpolate special values of certain vector-weight ${C}^{\infty }$ automorphic forms, including Eisenstein series, as their weights vary. This completes a key step toward the construction of certain $p$-adic $L$-functions.

We also explain how to extend our methods to the case of Siegel modular forms and how to recover Nicholas Katz’s $p$-adic families of Eisenstein series for Hilbert modular forms.

Keywords
Eisenstein measure, $p$-adic modular forms, $p$-adic automorphic forms, Eisenstein series, Siegel modular forms, automorphic forms on unitary groups
Mathematical Subject Classification 2010
Primary: 11F03
Secondary: 11F33, 11F30, 11F55, 11F85, 11F46