The modular parametrization of an elliptic curve over $\mathbb{Q}$ (and maybe over a number field in general?) is well-known; also for an elliptic curve over global function field with some condition (having split multiplicative reduction at some place), one also has an analogue of modular parametrization using Drinfeld modular variety in the function field case.

My main question is: Is there a version, over global function field, of modular parametrization using shtukas?

By the way, I read the survey ''Elliptic Curves and Analogies Between Number Fields and Function Fields'' by Dough Ulmer where he mentioned that there is a work by him entitled "Automorphic forms on GL2 over function fields and Gross–Zagier theorems'', but I could not find it. Has anyone read this paper and know where can I find it?