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On the minimum modulus of a multiple Dirichlet series with monotone coefficients

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Abstract

We establish conditions under which the relation M(x, F) ∼ Μ(x, F) ∼ m(x, F) holds except for a small set, as ¦x¦→ +∞ for an entire function F(z) of several complex variables z ∃ ℂ (p≥2) represented by a Dirichlet series, where M(x, F) = sup{¦F(x+iy¦: y ∃ ℝp}, m(x, F) = inf{¦F(x+iy)¦: y ∃ ℝp} Μ(x, F) being the maximal term of the Dirichlet series, and x ∃ ℝp.

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Literature cited

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Authors
  1. M. R. Lutsishin
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  2. O. B. Skaskiv
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Additional information

Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 21–25.

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Lutsishin, M.R., Skaskiv, O.B. On the minimum modulus of a multiple Dirichlet series with monotone coefficients. J Math Sci 96, 2957–2960 (1999). https://doi.org/10.1007/BF02169687

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  • DOI: https://doi.org/10.1007/BF02169687

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