On endoscopic p-adic automorphic forms for SL(2)

TL;DR

This paper demonstrates the existence of non-classical p-adic automorphic eigenforms for SL(2) by employing endoscopy and eigenvariety geometry, revealing forms that may correspond to non-automorphic members of classical L-packets.

Contribution

It introduces new non-classical cohomological p-adic automorphic forms for SL(2) using endoscopy and eigenvarieties, expanding understanding of automorphic forms.

Findings

Existence of non-classical p-adic automorphic eigenforms for SL(2)

Connection to non-automorphic members of classical L-packets

Use of endoscopy and eigenvariety geometry

Abstract

We show the existence of some non-classical cohomological p-adic automorphic eigenforms for SL(2) using endoscopy and the geometry of eigenvarieties. These forms seem to account for some non-automorphic members of classical global L-packets.