Abstract
Let \(\mathbb{L}\) be a complete ultrametric field of residue characteristic \(0\) and let \(F(x)=\sum_{i=1}^kf_i(x)exp(\omega_ix)\), where each \(f_i\in L[x]\), \(\omega_i\in \mathbb{L}\), \(|\omega_i|<1\). The number of zeros of \(F\) in the unit disk is bounded by \(n-1\) where \(n=\sum_{i=1}^k \deg(f_i)+k\).
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Acknowledgments
I am very grateful to the anonymous referee who pointed out me several misprints.
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Escassut, A. Number of Zeros of Exponential Polynomials in Zero Residue Characteristic. P-Adic Num Ultrametr Anal Appl 15, 81–83 (2023). https://doi.org/10.1134/S2070046623010053
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DOI: https://doi.org/10.1134/S2070046623010053