p-adic Siegel Eisenstein series of degree two
p-adic Siegel Eisenstein series of degree two
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p-adic 西格尔·爱森斯坦二级系列
DOI：
10.1016/j.jnt.2012.01.001
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发表时间：
2012
影响因子：
0.7
通讯作者：
Sho Takemori
中科院分区：
文献类型：
--
作者：
T.Kawahara;M.Sugita;M.Hagiwara;Y.Yamanishi;F.Arai;Sho Takemori
本文证明了具有任意导体的本原特征的二次Siegel-Eisenstein级数的Fourier系数的一个显式公式。证明了存在由二次Siegel-Eisenstein级数构成的p-adic解析族，并且二次Siegel-Eisenstein级数的某个p-adic极限实际上是二次Siegel-Eisenstein级数.
We prove an explicit formula for Fourier coefficients of Siegel–Eisenstein series of degree two with a primitive character of any conductor. Moreover, we prove that there exists the p-adic analytic family which consists of Siegel–Eisenstein series of degree two and a certain p-adic limit of Siegel–Eisenstein series of degree two is actually a Siegel–Eisenstein series of degree two.