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Non-cuspidal Bianchi modular forms and Katz $p$-adic $L$-functions (2302.13758v4)
Published 27 Feb 2023 in math.NT
Abstract: Let $K$ be an imaginary quadratic field. In this article, we construct $p$-adic $L$-functions of non-cuspidal Bianchi modular forms by introducing the notions of $C$-cuspidality and partial Bianchi modular symbols. When $p$ splits in $K$, we focus on $p$-adic $L$-functions of non-cuspidal base change Bianchi modular forms, showing that they factor as products of two Katz $p$-adic $L$-functions.