Skew-invariant curves and the algebraic independence of Mahler functions

Alice Medvedev, Khoa Dang Nguyen, Thomas Scanlon

For $p\in {\mathbb{Q}}_{+}\setminus \{1\}$ a positive rational number different from one, we say that the Puisseux series $f\in \mathbb{C}((t){)}^{\text{alg}}$ is $p$-Mahler of n…