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…
When any four solutions are independent
James Freitag
We show that if any four distinct solutions of a rational difference equation are algebraically independent, then any number of distinct solutions to the equation are independent.…
Finite-dimensional differential-algebraic permutation groups
James Freitag, Léo Jimenez, Rahim Moosa
Several structural results about permutation groups of finite rank definable in differentially closed fields of characteristic zero (and other similar theories) are obtained. In pa…