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2013 Fourier–Jacobi coefficients of Eisenstein series on unitary groups
Bei Zhang
Algebra Number Theory 7(2): 283-337 (2013). DOI: 10.2140/ant.2013.7.283


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.


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Bei Zhang. "Fourier–Jacobi coefficients of Eisenstein series on unitary groups." Algebra Number Theory 7 (2) 283 - 337, 2013.


Received: 17 January 2011; Revised: 3 February 2012; Accepted: 3 March 2012; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1319.11027
MathSciNet: MR3123640
Digital Object Identifier: 10.2140/ant.2013.7.283

Primary: 11F55
Secondary: 11F27 , 11F30 , 11R23

Keywords: doubling method , Eisenstein series , Fourier–Jacobi expansion , Iwasawa main conjecture , nonvanishing modulo $p$ , unitary groups

Rights: Copyright © 2013 Mathematical Sciences Publishers

Vol.7 • No. 2 • 2013
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