Algebraic number theory and diophantine geometry:
My research focuses on the arithmetic of Drinfeld modules. In particular, I am interested in Drinfeld modular varieties, Drinfeld modular forms, and automorphic forms of Drinfeld type. Recently, I have been working on equidistribution problems over global function fields and exploring their potential applications.
I am also deeply interested in the study of elliptic curves and rational points, especially from an arithmetic and geometric perspective.
Multifractal analysis of power means for the Schneider map on pZ_p. (with Nicolás Arévalo-Hurtado) Submitted. arXiv:2605.05484
Asymptotic distribution of CM points on the reduction of the Drinfeld modular curve. (with Patricio Pérez-Piña) Submitted. arXiv:2604.05069
The Lyapunov spectrum for Schneider map on pZ_p. (with Nicolás Arévalo-Hurtado) Submitted. arXiv:2601.05915
Explicit Zsigmondy bounds for families of Drinfeld modules of rank 2. Finite fields and their applications (Recommended for publication). arXiv:2505.04213
Counting algebraic points of bounded degree on curves. J. Number Theory (accepted). arXiv:2505.04219
Equidistribution of Hecke orbits on the Picard group of definite Shimura curves. (with Patricio Pérez-Piña) J. Number Theory 278 (2026), 715–725.
Fixed points of endomorphisms of complex tori (with Robert Auffarth) J. Algebra 507 (2018), 428-438
Fitting ideals of CM Drinfeld modules of rank 2.
On some Diophantine and Ergodic properties of the Schneider map over function fields. (with Nicolás Arévalo-Hurtado and Claudio Bravo)
On Drinfeld modular forms over P^1. (with Claudio Bravo)
Patricio Pérez-Piña, Department of Mathematical Sciences, University of Copenhagen, Denmark.
Nicolás Arévalo-Hurtado Universidad Escuela Colombiana de Ingeniería Julio Garavito, Bogotá, Colombia.
Robert Auffarth Universidad de Chile.
Claudio Bravo Universidad de Talca, Chile.