#### Vol. 14, No. 7, 2020

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$p$-adic Asai $L$-functions of Bianchi modular forms

### David Loeffler and Chris Williams

Vol. 14 (2020), No. 7, 1669–1710
##### Abstract

The Asai (or twisted tensor) $L$-function of a Bianchi modular form $\Psi$ is the $L$-function attached to the tensor induction to $ℚ$ of its associated Galois representation. When $\Psi$ is ordinary at $p$ we construct a $p$-adic analogue of this $L$-function: that is, a $p$-adic measure on ${ℤ}_{p}^{×}$ 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.

##### Keywords
Asai L-function, p-adic L-function, Bianchi modular form, Betti-Eisenstein classes, Iwasawa theory
##### Mathematical Subject Classification 2010
Primary: 11F67
Secondary: 11F41, 11F85, 11M41, 11S40