5 papers
The Pila-Zannier strategy for Drinfeld modules and Drinfeld modular curves
Gal Binyamini, Dmitry Novikov, Francesco Maria Saettone
We extend the Pila-Zannier strategy to Drinfeld modules: we prove analogues of the Manin-Mumford theorem for a product of two Drinfeld modules of equal rank, and of the André-Oort…
Procounting measures and the Bateman--Horn conjecture
Luca Demangos, Ignazio Longhi, Francesco Maria Saettone
Let be the ring of -integers in a global field and $\da$ its profinite completion. We propose a profinite version of the Bateman--Horn conjecture over and provide a firs…
Duke for Drinfeld
Francesco Maria Saettone
We prove a function field analogue of Duke's equidistribution theorem for CM points, in the setting of Drinfeld--Stuhler modular curves. Our results thus extend, to the Drinfeld se…
A note on equidistribution on a product of Shimura curves and André--Oort
Francesco Maria Saettone
In this short note we show that Galois orbits of CM points equidistribute on a product of non-isomorphic Shimura curves by applying the adelic toral-packet equidistributio…
Equidistribution of CM points on Shimura Curves and ternary theta series
Francesco Maria Saettone
We prove an equidistribution statement for the reduction of Galois orbits of CM points on the special fiber of a Shimura curve over a totally real field, considering both the split…