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Growth along a ray, distribution of the zeros of an entire function of finite order with respect to the argument, and a uniqueness theorem

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Abstract

For an entire function f of normal type and order ρ > 0 the asymptotic behavior of the quantity

$$l_f (R, \varphi ) = \int\limits_l^R {\frac{{ln|f(re^{l\varphi } )|}}{{r^{\rho + 1} }}} dr$$

and its connection with the distribution of the zeros of the function f with respect to the arguments are investigated.

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Authors
  1. A. F. Grishin
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  2. M. L. Sodin
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Additional information

Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 50, pp. 47–61, 1988.

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Grishin, A.F., Sodin, M.L. Growth along a ray, distribution of the zeros of an entire function of finite order with respect to the argument, and a uniqueness theorem. J Math Sci 49, 1269–1279 (1990). https://doi.org/10.1007/BF02209172

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  • DOI: https://doi.org/10.1007/BF02209172

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