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

Eischen, Ellen

doi:10.2140/ant.2014.8.2433

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

Ellen Eischen

Vol. 8 (2014), No. 10, 2433–2469

DOI: 10.2140/ant.2014.8.2433

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

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

Vol. 8, No. 10, 2014