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

Vlad Serban

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

Number Theory 2021-07-14 v2

Authors: Vlad Serban

Abstract

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.

Keywords

p-adic families bianchi modular forms automorphic forms imaginary quadratic fields finiteness cohomology

Cite

@article{arxiv.1902.03217,
  title  = {A finiteness result for $p$-adic families of Bianchi modular forms},
  author = {Vlad Serban},
  journal= {arXiv preprint arXiv:1902.03217},
  year   = {2021}
}

Comments

22 pages, v2: minor edits and corrected some sign or Galois conjugate errors in Table 2, adapting the proof of Prop 4.5 accordingly. To appear in Journal of Number Theory

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

Abstract

Keywords

Cite

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