Corpus ID: 224724714

Algebraic independence and linear difference equations.

@article{Adamczewski2020AlgebraicIA,
  title={Algebraic independence and linear difference equations.},
  author={B. Adamczewski and T. Dreyfus and C. Hardouin and Michael Wibmer},
  journal={arXiv: Number Theory},
  year={2020}
}
We consider pairs of automorphisms $(\phi,\sigma)$ acting on fields of Laurent or Puiseux series: pairs of shift operators $(\phi\colon x\mapsto x+h_1, \sigma\colon x\mapsto x+h_2)$, of $q$-difference operators $(\phi\colon x\mapsto q_1x,\ \sigma\colon x\mapsto q_2x)$, and of Mahler operators $(\phi\colon x\mapsto x^{p_1},\ \sigma\colon x\mapsto x^{p_2})$. Given a solution $f$ to a linear $\phi$-equation and a solution $g$ to a linear $\sigma$-equation, both transcendental, we show that $f$ and… Expand
3 Citations

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