p-ADIC L-FUNCTIONS FOR ORDINARY FAMILIES ON SYMPLECTIC GROUPS

被引：10

作者：

Liu, Zheng ^{[1
]}

机构：

[1] McGill Univ, Dept Math & Stat, Burnside Hall Room 1248,805 Sherbrooke St West, Montreal, PQ H3A 0B9, Canada

来源：

JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU | 2020年 / 19卷 / 04期

关键词：

p-adic L-functions; doubling method; ordinary families of Siegel modular forms; GALOIS REPRESENTATIONS; EISENSTEIN SERIES; ZETA-FUNCTIONS; SIEGEL; FORMS;

D O I：

10.1017/S1474748018000415

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct the p-adic standard L-functions for ordinary families of Hecke eigensystems of the symplectic group Sp(2n)(/Q) using the doubling method. We explain a clear and simple strategy of choosing the local sections for the Siegel Eisenstein series on the doubling group Sp(4n)(/Q), which guarantees the nonvanishing of local zeta integrals and allows us to p-adically interpolate the restrictions of the Siegel Eisenstein series to Sp(2n)(/Q), x Sp(2n)(/Q).

引用

页码：1287 / 1347

页数：61

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