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Number of Zeros of Exponential Polynomials in Zero Residue Characteristic
p-Adic Numbers, Ultrametric Analysis and Applications Pub Date : 2023-05-10 , DOI: 10.1134/s2070046623010053 Alain Escassut
更新日期：2023-05-11
p-Adic Numbers, Ultrametric Analysis and Applications Pub Date : 2023-05-10 , DOI: 10.1134/s2070046623010053 Alain Escassut
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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