Abstract
We show that if an exponential polynomial \(\sum _{i=1}^m P_i(z)e^{Q_i(z)}\), where \(P_i\), \(Q_i\in \mathbb C[z]\), is a dth power, \(d\ge 2\), 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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Chia-Liang Sun was supported in part by Taiwan’s MoST Grant 107-2115-M-001-013-MY2, and Julie Tzu-Yueh Wang was supported in part by Taiwan’s MoST Grant 108-2115-M-001-001-MY2.
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Guo, J., Sun, CL. & Wang, J.TY. On the dth Roots of Exponential Polynomials and Related Problems Arising from the Green–Griffiths–Lang Conjecture. J Geom Anal 31, 5201–5218 (2021). https://doi.org/10.1007/s12220-020-00475-2
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DOI: https://doi.org/10.1007/s12220-020-00475-2