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On the zeros of a special sequence of polynomials


Author: K. Mahler
Journal: Math. Comp. 39 (1982), 207-212
MSC: Primary 12D10; Secondary 30C15, 33A40
DOI: https://doi.org/10.1090/S0025-5718-1982-0658225-3
MathSciNet review: 658225
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Abstract: The zeros of the polynomials $ {P_n}(z) = \Sigma _{k = 0}^{n - 1}{z^{{2^k}}}$ are studied and a number of open questions are discussed.


References [Enhancements On Off] (What's this?)

  • [1] R. J. Evans, "Generalized cyclotomic periods," Proc. Amer. Math. Soc., v. 81, 1981, pp. 207-212. MR 593458 (82f:10050)
  • [2] I. L. Fuchs, "Über die Perioden, welche aus den Wurzeln der Gleichung $ {\omega ^n} = 1$ gebildet sind," J. Reine Angew. Math., v. 61, 1863, 374-386.
  • [3] R. Jentsch, Untersuchungen zur Theorie der Folgen analytischer Funktionen, Inauguraldissertation Berlin, 1914, 39 s.
  • [4] E. Landau, Darstellung und Begründung einiger neuen Ergebnisse der Funktionentheorie, Springer-Verlag, Berlin, 1916.
  • [5] K. Mahler, "On a special function," J. Number Theory, v. 12, 1980, pp. 20-26. MR 566865 (81c:30006)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1982-0658225-3
Article copyright: © Copyright 1982 American Mathematical Society

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