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arXiv · 2302.13758

Non-cuspidal Bianchi modular forms and Katz $p$-adic $L$-functions

Luis Santiago Palacios
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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.

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Luis Santiago Palacios. 2023-02-27. Non-cuspidal Bianchi modular forms and Katz $p$-adic $L$-functions. https://doi.org/10.1007/s00209-025-03694-x

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