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Asymptote of some entire exponential-type functions with zeros on spirals
S. K. Balashov Rostov State University
Abstract:
The author considers the Weierstrass canonical product of the first kind $\Pi(z)$, all roots of which lie on a spiral with equation in polar coordinates $(r,\Phi):\Phi=\ln\ln r$. With certain additional conditions on the roots, the asymptote is found for the function $\ln\{e^{Az}\Pi(z)\}$ ($A$ is some constant) in the complex plane cut along the spiral $\Phi=\ln\ln r$. The result is applied to the question of the sufficient condition for the satisfaction of an inequality for exponential-type functions, used in questions of the Dirichlet-series representation of analytic functions.
Received: 15.11.1971
Citation:
S. K. Balashov, “Asymptote of some entire exponential-type functions with zeros on spirals”, Mat. Zametki, 14:2 (1973), 173–184; Math. Notes, 14:2 (1973), 658–664
Linking options:
https://www.mathnet.ru/eng/mzm7246 https://www.mathnet.ru/eng/mzm/v14/i2/p173
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Abstract page: | 172 | Full-text PDF : | 75 | First page: | 1 |
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