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, Ruyong1,2 ; Feng, Shuang 1; Shen, Li-Yong 1
	2022-08-01
发表期刊	ADVANCES IN APPLIED MATHEMATICS
ISSN	0196-8858
卷号	139 页码:28
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
关键词	Height Algebraic curve Riemann-Roch space
DOI	10.1016/j.aam.2022.102373
收录类别	SCI
语种	英语
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
WOS类目	Mathematics, Applied
WOS记录号	WOS:000807970700004
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/61530
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.