## arXiv Analytics

### arXiv:1902.03217 [math.NT]AbstractReferencesReviewsResources

#### A finiteness result for $p$-adic families of Bianchi modular forms

Published 2019-02-08Version 1

We study $p$-adic families of cohomological automorphic forms for ${\mathrm{GL}}(2)$ over imaginary quadratic fields and prove that families interpolating a Zariski-dense set of classical cuspidal automorphic forms only occur under very restrictive conditions. We show how to computationally determine when this is not the case and establish concrete examples of families interpolating only finitely many Bianchi modular forms.

Representing Primes as the Form $x^2+ny^2$ in Some Imaginary Quadratic Fields