Algebraic independence of infinite series

TL;DR

This paper establishes conditions under which infinite series of rational numbers are algebraically independent, and applies these results to derive new insights on irrationality and linear independence over the rationals.

Contribution

It provides novel criteria for algebraic independence of infinite series and extends these to results on irrationality and linear independence.

Findings

Conditions for algebraic independence of series

New results on irrationality of certain series

Insights into Q-linear independence of series

Abstract

We give conditions on a finite set of series of rational numbers to ensure that they are algebraically independent. Specialising our results to polynomials of lower degree, we also obtain new results on irrationality and $mathbb{Q}$-linear independence of such series.