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Publication
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| Title of Article |
Bounds on the lengths of certain series expansions |
| Date of Acceptance |
28 April 2018 |
| Journal |
| Title of Journal |
Journal of Physics: Conference series (JPCS) |
| Standard |
SCOPUS |
| Institute of Journal |
Institute of Physics Publishing |
| ISBN/ISSN |
1742-6588, 1742-6596 |
| Volume |
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| Issue |
1132 |
| Month |
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| Year of Publication |
2018 |
| Page |
1-8 |
| Abstract |
In the real number field, there are several unique series expansions for each A \in (0,1). Of interest are the Sylvester and alternating Sylvester series expansions since both expansions are finite if and only if A is rational. We obtain upper bounds on the length of rational A \in (0,1) and lower bound on the length of certain classes of rational numbers. In the power series fi elds, let F_q denote the finite fi eld of q elements, let p(x) be an irreducible polynomial in F_q[x], and let F_q((p(x))), respectively, F_q((1/x)) be the completions of F_q(x) with respect to the p(x)-adic valuation, respectively, the infi nite valuation. It is known that each A \in F_q((p(x))), respectively, F_q((1/x)), subject to a technical assumption, has a unique Oppenheim series expansion, and such expansion is fi nite if and only if A \in F_q(x). Upper
bounds on the length of these series expansions for A \in Fq(x) are also derived. |
| Keyword |
Sylvester series; alternating-Sylvester series; rationality; upper bound; lower bound; Oppenheim series; rational function field; function field. |
| Author |
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| Reviewing Status |
มีผู้ประเมินอิสระ |
| Status |
ตีพิมพ์แล้ว |
| Level of Publication |
นานาชาติ |
| citation |
true |
| Part of thesis |
true |
| Attach file |
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| Citation |
0
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Journal Publication
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