Advanced Search

The purpose of this work is to carry out the first step in our four-step program towards the main conjecture for ${\text{GL}}_2\times {𝒦}^{\times }$ by the method of Eisenstein congruence on $GU(3,1)$, where $𝒦$ is an imaginary quadratic field. We construct a $p$-adic family of ordinary Eisenstein series on the group of unitary similitudes $GU(3,1)$ with the constant term which is basically the product of the Kubota-Leopodlt $p$-adic $L$-function and a $p$-adic $L$-function for ${\text{GL}}_2\times {𝒦}^{\times }$. This construction also provides a different point of view of $p$-adic $L$-functions...