A Determinantal Approach to Irrationality

@article{Zudilin2015ADA,
  title={A Determinantal Approach to Irrationality},
  author={W. Zudilin},
  journal={Constructive Approximation},
  year={2015},
  volume={45},
  pages={301-310}
}
  • W. Zudilin
  • Published 2015
  • Mathematics
  • Constructive Approximation
It is a classical fact that the irrationality of a number $$\xi \in \mathbb R$$ξ∈R follows from the existence of a sequence $$p_n/q_n$$pn/qn with integral $$p_n$$pn and $$q_n$$qn such that $$q_n\xi -p_n\ne 0$$qnξ-pn≠0 for all n and $$q_n\xi -p_n\rightarrow 0$$qnξ-pn→0 as $$n\rightarrow \infty $$n→∞. In this paper, we give an extension of this criterion in the case when the sequence possesses an additional structure; in particular, the requirement $$q_n\xi -p_n\rightarrow 0$$qnξ-pn→0 is weakened… Expand
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