On a $p$-adic extension of the Jacquet-Langlands correspondence to weight 1

Abstract

We consider a novel version of the classical Jacquet-Langlands {correspondence}, explore a $p$-adic extension of the Jacquet-Langlands correspondence, and as an explicit example we find an overconvergent automorphic form of weight~1 which corresponds to a classical modular form of weight~1, using both experimental and theoretical methods.

17 pages

References in corpus (1)

• Spectral expansions of overconvergent modular functions