On a theorem of Serret on continued fractions

A classical theorem in continued fractions due to Serret shows that for any two irrational numbers x and y related by a transformation γ in PGL ( 2 , Z ) there exist s and t for which the complete quotients x s and y t coincide. In this paper we give an upper bound in terms of γ for the smallest ind...

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Bibliographic Details
Published in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2016-09, Vol.110 (2), p.379-384
Main Author: Bengoechea, Paloma
Format: Article
Language:English
Subjects:
Applications of Mathematics
Formulas (mathematics)
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Quotients
Texts
Theorems
Theoretical
Transformations
Upper bounds
Citations: Items that this one cites
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Summary:A classical theorem in continued fractions due to Serret shows that for any two irrational numbers x and y related by a transformation γ in PGL ( 2 , Z ) there exist s and t for which the complete quotients x s and y t coincide. In this paper we give an upper bound in terms of γ for the smallest indices s and t .
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-015-0238-2