Volume 5 (2022)
Roques, Julien;  Singer, Michael F.
On the algebraic dependence of holonomic functions
Annales Henri Lebesgue, Volume 5 (2022), pp. 141-177

Metadata

DOI10.5802/ahl.120
Keywords Linear Differential Equations ,  Differential Galois Theory ,  Algebraic Relations ,  Iterated Integrals ,  Hypergeometric Functions

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.


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