Vol. 7, No. 2, 2013

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Fourier–Jacobi coefficients of Eisenstein series on unitary groups

Bei Zhang

Vol. 7 (2013), No. 2, 283–337
Abstract

This paper studies the Fourier–Jacobi expansions of Eisenstein series on U(3,1). I relate the Fourier–Jacobi coefficients of the Eisenstein series with special values of L-functions. This relationship can be applied to verify the existence of certain Eisenstein series on U(3,1) that do not vanish modulo p. This is a crucial step towards one divisibility of the main conjecture for GL2 × K× using the method of Eisenstein congruences.

Keywords
Iwasawa main conjecture, unitary groups, Eisenstein series, Fourier–Jacobi expansion, doubling method, nonvanishing modulo $p$
Mathematical Subject Classification 2010
Primary: 11F55
Secondary: 11F30, 11F27, 11R23
Milestones
Received: 17 January 2011
Revised: 3 February 2012
Accepted: 3 March 2012
Published: 25 April 2013
Authors
Bei Zhang
Northwestern University
Department of Mathematics
2033 Sheridan Rd.
Evanston, IL 60202
United States