Rational dynamical systems, S-units, and D-finite power series

doi:10.2140/ant.2021.15.1699

CSpace

	Rational dynamical systems, S-units, and D-finite power series
	Bell, Jason P.1; Chen, Shaoshi 2; Hossain, Ehsaan 3
	2021
发表期刊	ALGEBRA & NUMBER THEORY
ISSN	1937-0652
卷号	15 期号:7 页码:1699-1728
摘要	Let K be an algebraically closed field of characteristic zero, let G be a finitely generated subgroup of the multiplicative group of K, and let X be a quasiprojective variety defined over K. We consider K-valued sequences of the form a(n) = f (theta(n)(x(0))), where theta : X -> X and f : X -> P-1 are rational maps defined over K and x(0) is an element of X is a point whose forward orbit avoids the indeterminacy loci of theta and f. Many classical sequences from number theory and algebraic combinatorics fall under this dynamical framework, and we show that the set of n for which a(n) is an element of G is a finite union of arithmetic progressions along with a set of upper Banach density zero. In addition, we show that if a(n) is an element of G for every n and X is irreducible and the theta orbit of x is Zariski dense in X then there is a multiplicative torus G(m)(d) and maps Psi : G(m)(d) -> G(m)(d) and g : G(m)(d) -> G(m) such that a(n) = (g degrees Psi(n)) (y) for some y is an element of G(m)(d). We then obtain results about the coefficients of D-finite power series using these facts.
关键词	S-units D-finite series arithmetic dynamics algebraic groups orbits
DOI	10.2140/ant.2021.15.1699
收录类别	SCI
语种	英语
资助项目	NSERC[RGPIN-2016-03632] ; NSFC[11871067] ; NSFC[11688101] ; Fund of the Youth Innovation Promotion Association, CAS ; National Key Research and Development Project[2020YFA0712300]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000715749900004
出版者	MATHEMATICAL SCIENCE PUBL
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59553
专题	中国科学院数学与系统科学研究院
通讯作者	Bell, Jason P.
作者单位	1.Univ Waterloo, Dept Pure Math, Waterloo, ON, Canada 2.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Beijing, Peoples R China 3.Univ Toronto Mississauga, Dept Math & Computat Sci, Mississauga, ON, Canada
推荐引用方式 GB/T 7714	Bell, Jason P.,Chen, Shaoshi,Hossain, Ehsaan. Rational dynamical systems, S-units, and D-finite power series[J]. ALGEBRA & NUMBER THEORY,2021,15(7):1699-1728.
APA	Bell, Jason P.,Chen, Shaoshi,&Hossain, Ehsaan.(2021).Rational dynamical systems, S-units, and D-finite power series.ALGEBRA & NUMBER THEORY,15(7),1699-1728.
MLA	Bell, Jason P.,et al."Rational dynamical systems, S-units, and D-finite power series".ALGEBRA & NUMBER THEORY 15.7(2021):1699-1728.