| Title of Article |
On the Depth of Finite Schneider and Ruban Continued Fractions in F(x) |
| Date of Acceptance |
10 October 2018 |
| Journal |
| Title of Journal |
Southeast Asian Bulletin of Mathematics |
| Standard |
|
| Institute of Journal |
Southeast Asian Mathematical Society c/o Department of Mathematics Yunnan University |
| ISBN/ISSN |
0129-2021 |
| Volume |
|
| Issue |
|
| Month |
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| Year of Publication |
2019 |
| Page |
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| Abstract |
Let F be a field. Every rational function in F(x) has unique finite Schneider continued fraction (SCF) and Ruban continued fraction (RCF) in F((1/x)) and F((x)), the completions of F(x) with respect to the infinite and the x-adic valuations, respectively. The explicit constructions of these continued fractions are described. Upper bounds on the depth (length) of finite SCF in both F((1/x)) and F((x)) and of finite RCF in F((x)) are established. We also prove that the depth of the x-adic RCF of rational functions in F(x) evaluated at rational points is bounded, if F is finite. |
| Keyword |
Schneider continued fraction; Ruban continued fraction; Infinite valuation; x-adic valuation; Function field |
| Author |
|
| Reviewing Status |
มีผู้ประเมินอิสระ |
| Status |
ได้รับการตอบรับให้ตีพิมพ์ |
| Level of Publication |
นานาชาติ |
| citation |
true |
| Part of thesis |
true |
| Attach file |
|
| Citation |
0
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Publication
Journal Publication
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