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

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Algebraicity and the p-adic interpolation of special L-values for certain classical groups

  • 期刊论文

  • 发表日期：

    2025年5月14日

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  • Yubo Jin

摘要

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.