2019
DOI: 10.1515/crelle-2019-0033
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Greatest common divisors of analytic functions and Nevanlinna theory on algebraic tori

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 ou… Show more

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Cited by 10 publications
(15 citation statements)
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“…The result follows 21 We remark that we can use Corollary 6.6 instead of Theorem 1.1 to obtain a version of Theorem 1.6 for more general rational functions, not just x and y-coordinates.…”
Section: 2mentioning
confidence: 74%
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“…The result follows 21 We remark that we can use Corollary 6.6 instead of Theorem 1.1 to obtain a version of Theorem 1.6 for more general rational functions, not just x and y-coordinates.…”
Section: 2mentioning
confidence: 74%
“…There are several works in the literature on the problem of improving this trivial bound for the GCD counting function under various assumptions, see for instance [29,23,21]. For our purposes, the following will suffice.…”
Section: Gcd Counting Functions Given Non-constant Meromorphic Functmentioning
confidence: 99%
“…GCD in Nevanlinna theory. We recall the gcd counting function of two meromorphic functions and a gcd theorem with moving targets from [12].…”
Section: Theorem 26 ([4]mentioning
confidence: 99%
“…Our proof of Theorem 1.2 relies on the GCD theorem [12] of Levin and the third author and the machinery developed in [9]. The proof of Theorem 1.3 follows the ideas in [13] and [3] with extension to the moving situation.…”
Section: Introductionmentioning
confidence: 99%
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