- Title
- A determinantal approach to irrationality
- Creator
- Zudilin, Wadim
- Relation
- Funding BodyARCGrant NumberDP170100466
- Relation
- Constructive Approximation Vol. 45, Issue 2, p. 301-310
- Publisher Link
- http://dx.doi.org/10.1007/s00365-016-9333-7
- Publisher
- Springer
- Resource Type
- journal article
- Date
- 2017
- Description
- It is a classical fact that the irrationality of a number ξ∈R follows from the existence of a sequence pn/qn with integral pn and qn such that qnξ−pn≠0 for all n and qnξ−pn→0 as 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 qnξ−pn→0 is weakened. Some applications are given, including a new proof of the irrationality of π. Finally, we discuss analytical obstructions to extend the new irrationality criterion further and speculate about some mathematical constants whose irrationality is still to be established.
- Subject
- irrationality; rational approximation; π; Hankel determinant; Fekete–Chebyshev constant; transfinite diameter
- Identifier
- http://hdl.handle.net/1959.13/1387661
- Identifier
- uon:32649
- Identifier
- ISSN:0176-4276
- Rights
- This is a post-peer-review, pre-copyedit version of an article published in Constructive Approximation. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00365-016-9333-7.
- Language
- eng
- Full Text
- Reviewed
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