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Localization of the complex roots of a certain quasi-polynomial

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Abstract

The problem of localization of the zeros of the function w(z) = sinz + μsin(z/λ) on the complex plane is considered. Effective bounds for the imaginary parts |ℑ(ζ)| on nonreal zeros ζ of w(.) are obtained. It is demonstrated that, in the case of rational λ, ℜ(ζ) is quasiuniformly distributed.

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References

  1. V. K. Lashchenov and M. G. Sulimov, “The Roots of the Dispersion Equation for the Problem of Motion of an Elastic Strip,” Vestn. St. Peterb. Univ., Ser. 1 1(1), 82–88 (1995).

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  2. G. Pölya and G. Szegö, Problems and Theorems in Analysis (Springer, Berlin, 1964; Nauka, Moscow, 1978).

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Authors
  1. M. G. Sulimov
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Additional information

Original Russian Text © M.G. Sulimov, 2008, published in Vestnik Sankt-Peterburgskogo Universiteta. Seriya 1. Matematika, Mekhanika, Astronomiya, 2008, No. 1, pp. 78–84.

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Sulimov, M.G. Localization of the complex roots of a certain quasi-polynomial. Vestnik St.Petersb. Univ.Math. 41, 65–70 (2008). https://doi.org/10.3103/S1063454108010111

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  • DOI: https://doi.org/10.3103/S1063454108010111

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