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On the dth Roots of Exponential Polynomials and Related Problems Arising from the Green–Griffiths–Lang Conjecture
期刊文章   同儕審查

On the dth Roots of Exponential Polynomials and Related Problems Arising from the Green–Griffiths–Lang Conjecture

Ji Guo, Chia-Liang SunJulie Tzu-Yueh Wang
Journal of Geometric Analysis
2020

摘要

dth root Exponential polynomial Green–Griffiths–Lang conjecture Moving targets Geometry and Topology
We show that if an exponential polynomial ∑i=1mPi(z)eQi(z), where P i , Q i ∈ C[z] , is a dth power, d≥ 2 , of an entire function g, then g itself is also an exponential polynomial. We also study when a multivariable polynomial with moving targets of slow growth evaluated at unit arguments can be a dth power of an entire function. Finally, we formulate a boundary case of the Green–Griffiths–Lang conjecture for projective spaces with moving targets.

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