Special classes of functions

James Freitag; Léo Jimenez; Joel Nagloo

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arXiv · 2604.26187

Special classes of functions

James Freitag·Léo Jimenez·Joel Nagloo

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Abstract

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. These tools also allow us to give many examples of algebraic ordinary differential equations that do not have real Pfaffian solution on any open interval. We also give a sufficient condition for a function to be d-irreducible, in the sense of Nishioka. These characterizations are used to give several answers to questions of Bianconi (2016) and strengthen a theorem of Nguyen (2009).

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James Freitag, Léo Jimenez, Joel Nagloo. 2026-04-29. Special classes of functions. https://arxiv.org/abs/2604.26187

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