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

  • Zheng Liu (a1)

Abstract

We construct the $p$ -adic standard $L$ -functions for ordinary families of Hecke eigensystems of the symplectic group $\operatorname{Sp}(2n)_{/\mathbb{Q}}$ 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 $\operatorname{Sp}(4n)_{/\mathbb{Q}}$ , which guarantees the nonvanishing of local zeta integrals and allows us to $p$ -adically interpolate the restrictions of the Siegel Eisenstein series to $\operatorname{Sp}(2n)_{/\mathbb{Q}}\times \operatorname{Sp}(2n)_{/\mathbb{Q}}$ .

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

  • Zheng Liu (a1)

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