A semi-ordinary p-stabilization of Siegel Eisenstein series for symplectic groups and its p-adic interpolation

2012/07/01 by Hisa-aki Kawamura, Kawamura, Hisa-aki
Mathematics · #11F30 #11F33(secondary) #11F46(primary) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1207.0198

openalex publication_date 2012/07/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

For any rational prime p, we define a certain p-stabilization of holomorphic Siegel Eisenstein series for the symplectic group \rm Sp(2n)_/ℚ of an arbitrary genus n ≥ 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 Λ-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 Λ-adic Eisenstein series for \rm GL(2).

Citations

• On certain constructions of p-adic families of Siegel modular forms of even genus
• On ordinary ?-adic representations associated to modular forms

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