2 citations · 2 across the 10 of their papers we have counts for
11 papers
Ax-Schanuel for the Drinfeld -function
Gal Binyamini, Dmitry Novikov, Francesco Maria Saettone
We prove an analog of the Ax-Schanuel theorem for the Drinfeld -function in odd characteristic. Roughly speaking, if the graph of $\boldsymbol{j}\colonΩ^n\rightarrow\mathbb{A}^n…
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 its profinite completion. We propose a profinite version of the Bateman--Horn conjecture over and provid…
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…
Polylogarithmic motivic Chabauty-Kim for : the geometric step via resultants
David Jarossay, David T. -B. G. Lilienfeldt, Francesco Maria Saettone +2
Given a finite set of distinct primes, we propose a method to construct polylogarithmic motivic Chabauty-Kim functions for using resul…
Equidistribution of CM points on a Shimura Curve modulo a ramified prime
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 attached to some ramified p…
The fundamental group of surfaces parametrizing cuboids
Benjamin Enriquez, David Jarossay, Francesco Maria Saettone +1
We prove that an irreducible projective complete intersection of dimension at least two with isolated singularities has trivial fundamental group. As an application, the surface $Υ…
Heights and transcendence of --adic continued fractions
Ignazio Longhi, Nadir Murru, Francesco Maria Saettone
Special kinds of continued fractions have been proved to converge to transcendental real numbers by means of the celebrated Subspace Theorem. In this paper we study the analogous $…
Coset topologies on and arithmetic applications
Ignazio Longhi, Yunzhu Mu, Francesco Maria Saettone
We provide a construction which covers as special cases many of the topologies on integers one can find in the literature. Moreover, our analysis of the Golomb and Kirch topologies…