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arXiv · 1602.01776

p-adic L-functions for unitary groups

Ellen Eischen·Michael Harris·Jianshu Li·Christopher Skinner
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Abstract

This paper completes the construction of $p$-adic $L$-functions for unitary groups. More precisely, in 2006, the last three named authors proposed an approach to constructing such $p$-adic $L$-functions (Part I). Building on more recent results, including the first named author's construction of Eisenstein measures and $p$-adic differential operators, Part II of the present paper provides the calculations of local $\zeta$-integrals occurring in the Euler product (including at $p$). Part III of the present paper develops the formalism needed to pair Eisenstein measures with Hida families in the setting of the doubling method.

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Ellen Eischen, Michael Harris, Jianshu Li, Christopher Skinner. 2016-02-04. p-adic L-functions for unitary groups. https://doi.org/10.1017/fmp.2020.4

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