4 papers
Families of Unit Equations and Exponential Diophantine Problems via Integral Points
Julie Tzu-Yueh Wang, Zheng Xiao
This paper investigates the distribution of integral points on projective varieties via two distinct methods: the Ru-Vojta theorem and our higher-dimensional generalization of the…
Hyperbolicity and GCD for n+1 divisors with non-empty intersection
Julie Tzu-Yueh Wang, Zheng Xiao
We study hyperbolicity for quasi-projective varieties where the boundary divisor consists of n+1 numerically parallel effective divisors on a complex projective variety of dimensio…
A New Diophantine Approximation Inequality on Surfaces and Its Applications
Keping Huang, Aaron Levin, Zheng Xiao
We prove a Diophantine approximation inequality for closed subschemes on surfaces which can be viewed as a joint generalization of recent inequalities of Ru-Vojta and Heier-Levin i…
Greatest common divisors for polynomials in almost units and applications to linear recurrence sequences
Zheng Xiao
We bound the greatest common divisor of two coprime multivariable polynomials evaluated at algebraic numbers, generalizing work of Levin, and going towards conjectured inequalities…