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Quasi-equivalence of heights in algebraic function fields of one variable
Feng, Ruyong1,2; Feng, Shuang1; Shen, Li-Yong1
AbstractFor 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
KeywordHeight Algebraic curve Riemann-Roch space
Indexed BySCI
Funding ProjectNSFC[11771433] ; NSFC[11688101] ; Beijing Natural Science Foundation[Z190004] ; National Key Research and Development Project[2020YFA0712300] ; Fundamental Research Funds for Central Universities
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000807970700004
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Document Type期刊论文
Corresponding AuthorFeng, Shuang
Affiliation1.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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