#### 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 $U\left(3,1\right)$. 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 $U\left(3,1\right)$ that do not vanish modulo $p$. This is a crucial step towards one divisibility of the main conjecture for ${GL}_{2}×{K}^{×}$ 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