The overconvergent Shimura lifting

TL;DR

This paper constructs a rigid-analytic map that interpolates the classical Shimura lifting, connecting half-integral weight and integral weight eigencurves in a p-adic setting.

Contribution

It introduces a novel rigid-analytic map interpolating the classical Shimura lifting between eigencurves.

Findings

Established a rigid-analytic map between eigencurves

Interpolates classical Shimura lifting in a p-adic context

Bridges half-integral and integral weight modular forms

Abstract

We construct a rigid-analytic map from the the author's half-integral weight cuspidal eigencurve to its integral weight counterpart that interpolates the classical Shimura lifting.