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5 papers
A differential approach to Ax-Schanuel, I
David Blázquez-Sanz, Guy Casale, James Freitag +1
In this paper, we prove several Ax-Schanuel type results for uniformizers of geometric structures; our general results describe the differential algebraic relations between the sol…
Special classes of functions
James Freitag, Léo Jimenez, Joel Nagloo
Using model theory and differential algebra, we give necessary conditions for algebraic ordinary differential equations to have a complex Pfaffian solution on some complex domain.…
On the number of independent solutions of algebraic differential equations
James Freitag, Omar León Sánchez, Wei Li +1
We prove a conjecture of Kumbhakar, Roy, and Srinivasan (2024) on the classification of order one differential equations, and a conjecture of Kumbhakar and Srinivasan (2025) on hig…
Categoricity and non-arithmetic Fuchsian groups
John Baldwin, Joel Nagloo
Let be a non-arithmetic Fuchsian group of the first kind with finite covolume, and let be a corresponding uniformizer. In this paper we introdu…
Algebraic independence of the solutions of the classical Lotka-Volterra system
Yutong Duan, Joel Nagloo
Let be distinct non-constant and non-degenerate solutions of the classical Lotka-Volterra system \begin{equation}\notag \begin{split} x'&= axy + bx\\ y…