On maximum modulus points and zero set of an entire function

Author
S.I.Fedynyak
Faculty of Mechanics and Mathematics,Ivan Franko National University of Lviv
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.
Keywords
maximum modulus point, zero set, entire function
DOI
doi:10.30970/ms.30.2.169-172
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.

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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
Volume
30
Issue
2
Year
2008
Journal
Matematychni Studii
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