P-adic asai L-functions of bianchi modular forms
Author(s)
Williams, Christopher
Loeffler, David
Type
Working Paper
Abstract
The Asai (or twisted tensor) L-function of a Bianchi modular form Ψ is the L-function attached to the tensor induction to ℚ of its associated Galois representation. In this paper, when Ψ 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.
Date Issued
2019-06-20
Citation
2019
Notes
Submitted to Algebra & Number Theory. We have received an initial referee report strongly recommending publication and have resubmitted following minor corrections. This is probably the best paper I am submitting for REF. It gives a completely new method for constructing p-adic L-functions via towers of Betti cohomology classes, and in the process applies this new method to give the first example of a p-adic Asai L-function. The method should apply more widely and in particular opens up new attacks on previously intractable problems, such as the construction of p-adic L-functions for GL(3), which we will consider in future work. Whilst not yet accepted formally, we have received positive verbal feedback from the editor at Algebra & Number Theory managing our paper, as well as a report strongly recommending publication. A&NT is widely regarded as the top journal specialising in number theory, and more generally is 'at a level surpassing all but the top four or five mathematics journals.'
Publication Status
Submitted