P-adic Asai L-functions of Bianchi modular forms

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.

arXiv commentFinal version, to appear in Algebra & Number Theory

References in corpus (8)

• Rankin--Eisenstein classes and explicit reciprocity laws
• Euler systems for Rankin--Selberg convolutions of modular forms
• Rankin--Eisenstein classes for modular forms
• Rankin--Eisenstein classes in Coleman families
• Galois representations attached to automorphic forms on GL_2 over CM fields
• Euler systems for Hilbert modular surfaces
• $P$-adic $L$-functions of Bianchi modular forms
• $\mathcal{L}$-invariants and exceptional zeros of Bianchi modular forms

Cited by in corpus (5)

• Spherical varieties and norm relations in Iwasawa theory
• $p$-adic Asai $L$-functions attached to Bianchi cusp forms
• Poles of p-adic Asai L-functions and distinguished representations
• P-adic Asai L-functions for quadratic Hilbert eigenforms
• P-adic L-functions for GL(3)