KMS Of Academy of mathematics and systems sciences, CAS
Quasi-equivalence of heights in algebraic function fields of one variable | |
Feng, Ruyong1,2; Feng, Shuang1; Shen, Li-Yong1 | |
2022-08-01 | |
Source Publication | ADVANCES IN APPLIED MATHEMATICS |
ISSN | 0196-8858 |
Volume | 139Pages:28 |
Abstract | For points (a, b) on an algebraic curve over a field K with height h, the asymptotic relation between h(a) and h(b) has been extensively studied in diophantine geometry. When K = k(t) is the field of algebraic functions in t over a field k of characteristic zero, Eremenko in 1998 proved the following quasi-equivalence for an absolute logarithmic height h in K: Given P is an element of K[X, Y] irreducible over K and is an element of > 0, there is a constant C only depending on P and E such that for each (a, b) is an element of K-2 with P (a, b) = 0, (1 - epsilon) deg(P, Y )h(b) - C <= deg(P, X)h(a)<= 1 +epsilon) deg(P, Y )h(b) + C. In this article, we shall give an explicit bound for the constant C in terms of the total degree of P, the height of P and E. This result is expected to have applications in some other areas such as symbolic computation of differential and difference equations. (C) 2022 Elsevier Inc. All rights reserved |
Keyword | Height Algebraic curve Riemann-Roch space |
DOI | 10.1016/j.aam.2022.102373 |
Indexed By | SCI |
Language | 英语 |
Funding Project | NSFC[11771433] ; NSFC[11688101] ; Beijing Natural Science Foundation[Z190004] ; National Key Research and Development Project[2020YFA0712300] ; Fundamental Research Funds for Central Universities |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied |
WOS ID | WOS:000807970700004 |
Publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/61530 |
Collection | 系统科学研究所 |
Corresponding Author | Feng, Shuang |
Affiliation | 1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China |
Recommended Citation GB/T 7714 | Feng, Ruyong,Feng, Shuang,Shen, Li-Yong. Quasi-equivalence of heights in algebraic function fields of one variable[J]. ADVANCES IN APPLIED MATHEMATICS,2022,139:28. |
APA | Feng, Ruyong,Feng, Shuang,&Shen, Li-Yong.(2022).Quasi-equivalence of heights in algebraic function fields of one variable.ADVANCES IN APPLIED MATHEMATICS,139,28. |
MLA | Feng, Ruyong,et al."Quasi-equivalence of heights in algebraic function fields of one variable".ADVANCES IN APPLIED MATHEMATICS 139(2022):28. |
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