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Algebraic interpretation of continued fractions

✍ Scribed by Yair Shapira

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
261 KB
Volume
78
Category
Article
ISSN
0377-0427

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✦ Synopsis

An alternative (equivalent) definition of continued fractions in terms of a group representation is introduced. With this definition, continued fractions are considered as sequences in a topological group, converging (in some sense) to its boundary. This point of view yields an alternative (equivalent) proof for Lane's convergence theorem for periodic continued fractions.

πŸ“œ SIMILAR VOLUMES

Diophantine Approximation Exponents and
Diophantine Approximation Exponents and Continued Fractions for Algebraic Power Series
✍ Dinesh S. Thakur πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 100 KB

For each rational number not less than 2, we provide an explicit family of continued fractions of algebraic power series in finite characteristic (together with the algebraic equations they satisfy) which has that rational number as its diophantine approximation exponent. We also provide some non-qu