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 Ψ is the L-function attached to the tensor induction to of its associated Galois representation. When Ψ is ordinary at p we construct a p-adic analogue of this L-function: that is, a p-adic measure on 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
Milestones
Received: 30 July 2018
Revised: 16 September 2019
Accepted: 10 March 2020
Published: 18 August 2020
Authors
David Loeffler
Mathematics Institute
University of Warwick
Coventry
United Kingdom
Chris Williams
Mathematics Institute
University of Warwick
Coventry
United Kingdom