Algebraicity and the $p$-adic Interpolation of Special $L$-values for certain Classical Groups

Yubo Jin

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arXiv · 2305.19113

Algebraicity and the $p$-adic Interpolation of Special $L$-values for certain Classical Groups

Yubo Jin

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Abstract

In this paper, we calculate the ramified local integrals in the doubling method and present an integral representation of standard $L$-functions for classical groups. We explicitly construct local sections of Eisenstein series such that the local ramified integrals represent certain ramified $L$-factors. As an application, we prove algebraicity of special $L$-values and construct $p$-adic $L$-functions for symplectic, unitary, quaternionic unitary and quaternionic orthogonal groups.

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Yubo Jin. 2023-05-30. Algebraicity and the $p$-adic Interpolation of Special $L$-values for certain Classical Groups. https://arxiv.org/abs/2305.19113

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