Algebraic independence of Mahler functions via radial asymptotics

@article{Brent2014AlgebraicIO,
  title={Algebraic independence of Mahler functions via radial asymptotics},
  author={Richard P. Brent and Michael Coons and Wadim Zudilin},
  journal={arXiv: Number Theory},
  year={2014}
}
We present a new method for algebraic independence results in the context of Mahler's method. In particular, our method uses the asymptotic behaviour of a Mahler function $f(z)$ as $z$ goes radially to a root of unity to deduce algebraic independence results about the values of $f(z)$ at algebraic numbers. We apply our method to the canonical example of a degree two Mahler function; that is, we apply it to $F(z)$, the power series solution to the functional equation $F(z)-(1+z+z^2)F(z^4)+z^4F(z… 

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