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arXiv · 1802.08207

P-adic Asai L-functions of Bianchi modular forms

David Loeffler·Chris Williams
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Abstract

The Asai (or twisted tensor) $L$-function of a Bianchi modular form $\Psi$ is the $L$-function attached to the tensor induction to $\mathbb{Q}$ of its associated Galois representation. In this paper, when $\Psi$ is ordinary at $p$ we construct a $p$-adic analogue of this $L$-function: that is, a $p$-adic measure on $\mathbb{Z}_p^\times$ that interpolates the critical values of the Asai $L$-function twisted by Dirichlet characters of $p$-power conductor. The construction uses techniques analogous to those used by Lei, Zerbes and the first author in order to construct an Euler system attached to the Asai representation of a quadratic Hilbert modular form.

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BibTeXRIS

David Loeffler, Chris Williams. 2018-02-22. P-adic Asai L-functions of Bianchi modular forms. https://doi.org/10.2140/ant.2020.14.1669

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