English

Algebraic independence of infinite series

Number Theory 2025-02-27 v1

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 mathbbQmathbb{Q}-linear independence of such series.

Keywords

Cite

@article{arxiv.2502.19079,
  title  = {Algebraic independence of infinite series},
  author = {Jaroslav Hancl and Mathias L. Laursen and Simon Kristensen},
  journal= {arXiv preprint arXiv:2502.19079},
  year   = {2025}
}