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P-adic asai L-functions of bianchi modular forms

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Title: P-adic asai L-functions of bianchi modular forms
Authors: Williams, C
Loeffler, D
Item 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.
Issue Date: 20-Jun-2019
URI: http://hdl.handle.net/10044/1/70716
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
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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