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.
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}
}