Extending meromorphic connections to coadmissible ̑𝒟-modules

Abstract We investigate when a meromorphic connection on a smooth rigid analytic variety 𝑋 gives rise to a coadmissible D⏜X\overparen{\mathcal{D}}_{X}-module, and show that this is always the case when the roots of the corresponding 𝑏-functions are all of positive type. We also use this theory to give an example of an integrable connection on the punctured unit disk whose pushforward is not a coadmissible module.