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A semi-ordinary $p$-stabilization of Siegel Eisenstein series for symplectic groups and its $p$-adic interpolation. (arXiv:1207.0198v4 [math.NT] UPDATED)
来源于:arXiv
For any rational prime $p$, we define a certain $p$-stabilization of
holomorphic Siegel Eisenstein series for the symplectic group ${\rm
Sp}(2n)_{/\mathbb{Q}}$ of an arbitrary genus $n \ge 1$. In addition, we derive
an explicit formula for the Fourier coefficients and conclude their $p$-adic
interpolation problems. Consequently, for any odd prime $p$, we deduce the
existence of a $\Lambda$-adic form (in the sense of A. Wiles, H. Hida and R.L.
Taylor) such that after taking a suitable constant multiple, it interpolates
$p$-adic analytic families of the above-mentioned $p$-stabilized Siegel
Eisenstein series with nebentypus characters locally trivial at $p$ and Siegel
Eisenstein series with nebentypus characters locally non-trivial at $p$
simultaneously. This can be viewed as a quite natural generalization of the
ordinary $\Lambda$-adic Eisenstein series for ${\rm GL}(2)$. 查看全文>>