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Functional equation of the $p$-adic $L$-function of Bianchi modular forms

Published 6 May 2021 in math.NT | (2105.02770v2)

Abstract: Let $K$ be an imaginary quadratic field with class number 1, in this paper we obtain the functional equation of the $p$-adic $L$-function of small slope $p$-stabilised Bianchi modular forms. Then, using $p$-adic families of Bianchi modular forms, we extend our result to $\Sigma$-smooth base-change Bianchi modular forms.

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