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Number of zeros of exponential functions. Polynomials (after A. J. van der Poorten). (Nombre de zéros des fonctions exponentielles. Polynômes (d’après A. J. van der Poorten).) (German) Zbl 0381.12010

Groupe d’Étude d’Anal. Ultramétr., 4e Année 1976/77, Exp. No. 9, 3 p. (1978).
Summary: The author shows that a method of the reviewer [Nederl. Akad. Wet., Proc., Ser. A 79, 46–49 (1976; Zbl 0318.30006)] is readily amended to yield an apparently best possible bound for the number of zeros of \(p\)-adic exponential polynomials in appropriate discs. This result had been clumsily missed by the reviewer in the cited paper, but was obtained by him subsequently by means of a considerably more complicated method [J. Aust. Math. Soc., Ser. A 22, 12–26 (1976; Zbl 0348.12022)].
[For the entire collection see Zbl 0362.00006.]

MSC:

11S05 Polynomials
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
Full Text: Numdam EuDML