On a theorem of Borel on diophantine approximation

A theorem of É. Borel’s asserts that one of any three consecutive convergents of a real number a , which we denote p q , satisfies the inequality a - p q < C q 2 with C = 1 5 . In this paper we give more precise information about the constant C .

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Bibliographic Details
Published in:The Ramanujan journal 2024-10, Vol.65 (2), p.897-915
Main Authors: Hančl, Jaroslav, Nair, Radhakrishnan
Format: Article
Language:English
Subjects:
Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
Real numbers
Theorems
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Description
Summary:A theorem of É. Borel’s asserts that one of any three consecutive convergents of a real number a , which we denote p q , satisfies the inequality a - p q < C q 2 with C = 1 5 . In this paper we give more precise information about the constant C .
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-024-00922-6