Greatest common divisors of analytic functions and Nevanlinna theory on algebraic tori
Complex Variables
2019-03-12 v1
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.
Keywords
Cite
@article{arxiv.1903.03876,
title = {Greatest common divisors of analytic functions and Nevanlinna theory on algebraic tori},
author = {Aaron Levin and Julie Tzu-Yueh Wang},
journal= {arXiv preprint arXiv:1903.03876},
year = {2019}
}