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Generalizing Turan’s main theorems on lower bounds for sums of powers. (English) Zbl 0264.30032

MSC:
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
30B10 Power series (including lacunary series) in one complex variable
30C10 Polynomials and rational functions of one complex variable
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
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[1] E. Makai, The first main theorem of P. Turán,Acta Math. Acad. Sci. Hung.,10 (1959), pp. 405–411. · Zbl 0097.03802
[2] R. Tijdeman, On van der Poorten’s proofs of the main theorems of Turán,On the distribution of values of certain functions, Ch. I, Ph. D. Thesis (Amsterdam, 1969).
[3] R. Tijdeman, On a generalisation of Turán’s main theorems, Ch. II Ph. D. Thesis op. cit. (Amsterdam, 1969).
[4] R. Tijdeman, Some theorems on general exponential polynomials, Ch. III Ph. D. Thesis op. cit. (Amsterdam, 1969).
[5] P. Turán,Eine neue Methode in der Analysis und deren Anwendungen (Akadémiai Kiadó, Budapest, 1953).
[6] A. J. Van der Poorten,Simultaneous algebraic approximation of functions, Ph. D. Thesis (The University of NSW, 1968).
[7] A. J. Van der Poorten, Generalisations of Turán’s main theorems on lower bounds for sums of powers,Bull. Aust. Math. Soc.,2 (1970), pp. 15–37. · Zbl 0179.07101
[8] A. J. Van der Poorten, A generalisation of Turán’s main theorems to binomials and logarithms,Bull. Aust. Math. Soc.,2 (1970), pp. 183–195. · Zbl 0192.39501
[9] A. J. Van der Poorten, A new result on the distribution of zeros of classes of exponential polynomials (unpublished manuscript).
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