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 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
Milestones
Received: 3 March 2014
Revised: 22 September 2014
Accepted: 3 November 2014
Published: 31 December 2014
Authors
Ellen Eischen
Department of Mathematics
The University of North Carolina at Chapel Hill
CB #3250
Chapel Hill, NC 27599-3250
United States