On maximum modulus points and zero set of an entire function |
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| Author |
fedynyak@yahoo.com
Faculty of Mechanics and Mathematics,Ivan Franko National University of Lviv
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| Abstract |
Let $f$ be an entire function. Let $w$ be a point such that $\vert f (w)\vert = \max \{\vert f (z)\vert : \vert z\vert = \vert w\vert \}$ and $R(w,f)$ be the distance between the point $w$ and the zero set of $f.$ We obtain asymptotic estimates for the function $R(w,f), \vert w\vert \to \infty,$ when $f$ is an entire function of arbitrary growth.
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| Keywords |
maximum modulus point, zero set, entire function
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| DOI |
doi:10.30970/ms.30.2.169-172
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Reference |
1. Ostrovskii I.V., Üreyen A.E. Distance between maximum modulus point and zero set for entire function// Complex Variables. -- 2003. -- V.48. -- P. 583--598.
2. Üreyen A.E. On maximum modulus point and the zero set for entire function// Computational Methods and Function Theory. -- 2004. -- V.4, №2. -- P.341--354. 3. Шеремета М.М. Про похідну цілої функцуії// Укр. мат. журн. -- 1988. -- Т.40, №2. -- P.188--192. 4. Macintyre A.J. Wiman's method and "flat regions" of integral functions// Quart. J. Math. -- 1938. -- V.9. -- P.81--88. |
| Pages |
169-172
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| Volume |
30
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| Issue |
2
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| Year |
2008
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| Journal |
Matematychni Studii
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| Full text of paper | |
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