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A semi-ordinary $p$-stabilization of Sie...
Kawamura, Hisa-aki...

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A semi-ordinary $p$-stabilization of Siegel Eisenstein series for symplectic groups and its $p$-adic interpolation by Kawamura, Hisa-aki ( Author )
Lemonjar Open Access
Australian National University
21-08-2023
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 ${\rm GL}(2)$.
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Article
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29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1207.0198
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