Greatest common divisors of analytic functions and Nevanlinna theory on algebraic tori
Aaron Levin,Julie Tzu-Yueh Wang +1 more
TLDR
In this article, the counting function of common zeros of two meromorphic functions in various contexts is studied and a general version of a conjectural "asymptotic gcd" inequality of Pasten and the second author is proved.Abstract:
We study upper bounds for the counting function of common zeros of two meromorphic functions in various contexts. The proofs and results are inspired by recent work involving greatest common divisors in Diophantine approximation, to which we introduce additional techniques to take advantage of the stronger inequalities available in Nevanlinna theory. In particular, we prove a general version of a conjectural "asymptotic gcd" inequality of Pasten and the second author, and consider moving targets versions of our results.read more
Citations
More filters
Journal ArticleDOI
Greatest common divisors with moving targets and consequences for linear recurrence sequences
Nathan Grieve,Julie Wang +1 more
TL;DR: In this paper, it was shown that the logarithmic greatest common divisor of moving multivariable polynomials evaluated at moving $S$-unit arguments is bounded.
Posted Content
On the Skolem problem and some related questions for parametric families of linear recurrence sequences
Alina Ostafe,Igor E. Shparlinski +1 more
TL;DR: In this paper, it was shown that in a parametric family of linear recurrence sequences with coefficients and characteristic roots, the Skolem problem is solvable for all but a set of vertices of bounded height in the algebraic closure of a number field.
Journal ArticleDOI
On the d th Roots of Exponential Polynomials and Related Problems Arising from the Green–Griffiths–Lang Conjecture
TL;DR: In this paper, it was shown that if an exponential polynomial with moving targets of slow growth evaluated at unit arguments can be a dth power of an entire function, then the entire function itself is also an exponential polynomial.
Journal ArticleDOI
Greatest common divisors of integral points of numerically equivalent divisors
Julie Tzu-Yueh Wang,Yu Yasufuku +1 more
TL;DR: In this paper, the authors generalize the G.C.D. results of Corvaja-Zannier and Levin on G_m^n$ to more general settings, and show that this height is small when evaluated at integral points with respect to a divisor.
Posted Content
Divisibility of polynomials and degeneracy of integral points
TL;DR: In this article, it was shown that simply connected quasi-projective varieties are pseudo-arithmetically hyperbolic, which generalizes results of Corvaja and Zannier in dimension 2 to arbitrary dimension.
References
More filters
Book
Introduction to Complex Hyperbolic Spaces
TL;DR: In this article, the negative Curvature on Line Bundles (NCLB) is used to define the normal families of the Disc in Pn Minus Hyperplanes.
Book
Nevanlinna Theory and Its Relation to Diophantine Approximation
TL;DR: Theorem of Faltings complex Hyperbolic Manifolds and Lang's Conjecture as mentioned in this paper is related to the moving target problems in the context of meromorphic functions.
BookDOI
Nevanlinna theory in several complex variables and Diophantine approximation
潤次郎 野口,Jörg Winkelmann +1 more
TL;DR: In this paper, Nevanlinna Theory of Meromorphic functions over function fields has been used to define differentiably non-degenerate Meromorphic Maps (DNMMs).
Book ChapterDOI
Diophantine Approximation and Nevanlinna Theory
TL;DR: It has been known that the branch of complex analysis known as Nevanlinna theory (also called value distribution theory) has many similarities with Roth's theorem on diophantine approximation.