Upper Bounds of GCD Counting Function for Holomorphic Maps
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In this paper, we give upper bounds for the gcd counting function(which is an analogue for the notion of gcd in the context of holomorphic maps) in various settings. As applications, we obtain analytic dependence of entire functions from the second main theorem and multiplicative dependence under the fundamental conjecture for entire curves.
KeywordsGcd counting function Analytic dependence Multiplicative dependence Second main theorem
Mathematics Subject Classification11A05 30D35 32A22 32H30
X. Liu was supported by NSFC11401381, G. Yu was supported by NSFC11671090.
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