Diophantine Approximation and Nevanlinna Theory

2010 ◽  
pp. 111-224 ◽  
Author(s):  
Paul Vojta
Keyword(s):  
Diophantine Approximation ◽  
Nevanlinna Theory

scholarly journals Greatest common divisors of analytic functions and Nevanlinna theory on algebraic tori

2020 ◽  
Vol 2020 (767) ◽  
pp. 77-107 ◽  
Author(s):  
Aaron Levin ◽  
Julie Tzu-Yueh Wang
Keyword(s):  
Diophantine Approximation ◽  
Nevanlinna Theory ◽  
Meromorphic Functions ◽  
Counting Function ◽  
Upper Bounds ◽  
General Version ◽  
Moving Targets ◽  
Algebraic Tori ◽  
Greatest Common Divisors ◽  
Common Zeros

AbstractWe 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.

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