English

On the algebraic dependence of holonomic functions

Commutative Algebra 2020-11-04 v1 Classical Analysis and ODEs Number Theory

Abstract

We study the form of possible algebraic relations between functions satisfying linear differential equations. In particular , if f and g satisfy linear differential equations and are algebraically dependent, we give conditions on the differential Galois group associated to f guaranteeing that g is a polynomial in f. We apply this to hypergeometric functions and iterated integrals.

Keywords

Cite

@article{arxiv.2011.01717,
  title  = {On the algebraic dependence of holonomic functions},
  author = {Julien Roques and Michael F. Singer},
  journal= {arXiv preprint arXiv:2011.01717},
  year   = {2020}
}
R2 v1 2026-06-23T19:53:09.379Z