Quasi-equivalence of heights in algebraic function fields of one variable

doi:10.1016/j.aam.2022.102373

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	Quasi-equivalence of heights in algebraic function fields of one variable
	Feng, Ruyong 1,2; Feng, Shuang 1; Shen, Li-Yong 1
刊名	ADVANCES IN APPLIED MATHEMATICS
	2022-08-01
卷号	139 页码:28
关键词	Height Algebraic curve Riemann-Roch space
ISSN号	0196-8858
DOI	10.1016/j.aam.2022.102373
英文摘要	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
资助项目	NSFC[11771433] ; NSFC[11688101] ; Beijing Natural Science Foundation[Z190004] ; National Key Research and Development Project[2020YFA0712300] ; Fundamental Research Funds for Central Universities
WOS研究方向	Mathematics
语种	英语
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
WOS记录号	WOS:000807970700004
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/61529]
专题	系统科学研究所
通讯作者	Feng, Shuang
作者单位	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
推荐引用方式 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.