Liang Chung Hsia
National Central University
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Featured researches published by Liang Chung Hsia.
Journal of The London Mathematical Society-second Series | 2000
Liang Chung Hsia
The closure of the periodic points of rational maps over a non-archimedean field is studied. An analogue of Montels theorem over non-archimedean fields is first proved. Then, it is shown that the (nonempty) Julia set of a rational map over a non-archimedean field is contained in the closure of the periodic points.
Crelle's Journal | 2005
Matthew Baker; Liang Chung Hsia
Abstract Let ϕ(z ) be a polynomial of degree at least 2 with coefficients in a number field K. Iterating ϕ gives rise to a dynamical system and a corresponding canonical height function ĥϕ , as defined by Call and Silverman. We prove a simple product formula relating the transfinite diameters of the filled Julia sets of ϕ over various completions of K, and we apply this formula to give a generalization of Bilu’s equidistribution theorem for sequences of points whose canonical heights tend to zero.
arXiv: Number Theory | 2015
Dragos Ghioca; Liang Chung Hsia; Thomas J. Tucker
Let X be a smooth curve defined over the algebraic numbers, let a,b be algebraic numbers, and let f_l(x) be an algebraic family of rational maps indexed by all l in X. We study whether there exist infinitely many l in X such that both a and b are preperiodic for f_l. In particular we show that if P,Q are polynomials over the algebraic numbers such that deg(P) >= 2+deg(Q), and there exists l such that a is periodic for P(x)/Q(x) + l, but b is not preperiodic for P(x)/Q(x) + l, then there exist at most finitely many l such that both a and b are preperiodic for P(x)/Q(x)+l. We also prove a similar result for certain two-dimensional families of endomorphisms of P^2.
Compositio Mathematica | 2000
Liang Chung Hsia; Jing Yu
AbstractLet K be a function field over finite field
Transactions of the American Mathematical Society | 2004
Liang Chung Hsia; Julie Tzu-Yueh Wang
Compositio Mathematica | 1996
Liang Chung Hsia
\mathbb{F}_q
Algebra & Number Theory | 2013
Dragos Ghioca; Liang Chung Hsia; Thomas J. Tucker
Journal de Theorie des Nombres de Bordeaux | 2009
Liang Chung Hsia; Joseph H. Silverman
and let
Journal of Number Theory | 2008
Liang Chung Hsia
Pacific Journal of Mathematics | 2011
Liang Chung Hsia; Joseph H. Silverman
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