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Author:
P. C. Fenton

Journal:
Proc. Amer. Math. Soc. **131** (2003), 1875-1880

MSC (2000):
Primary 30D15

DOI:
https://doi.org/10.1090/S0002-9939-02-06750-3

Published electronically:
November 6, 2002

MathSciNet review:
1955276

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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that if, for an entire function,

where , then

In the proof, the zeros of the function are redistributed to minimize the large values of .

**1.**Albert Baernstein II, A generalization of the cos theorem, Trans. Amer. Math. Soc.**193**(1974), 181-97. MR**49:9207****2.**R.P. Boas,*Entire Functions*(Academic Press, 1954). MR**16:914f****3.**E.T. Copson,*Theory of Functions of a Complex Variable*(Oxford, 1935).**4.**P.C. Fenton, A min-max theorem for sums of translates of a function, J. Math. Anal. App.**244**(2000), 214-222. MR**2001a:26007****5.**Bo Kjellberg, On the minimum modulus of entire functions of lower order less than one, Math. Scand.**8**(1960), 189-97. MR**23:A3264****6.**Bo Kjellberg, A theorem on the minimum modulus of entire functions, Math. Scand.**12**(1963), 5-11. MR**28:3158**

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Additional Information

**P. C. Fenton**

Affiliation:
Department of Mathematics, University of Otago, P.O. Box 56, Dunedin, New Zealand

DOI:
https://doi.org/10.1090/S0002-9939-02-06750-3

Received by editor(s):
February 7, 2002

Published electronically:
November 6, 2002

Communicated by:
Juha M. Heinonen

Article copyright:
© Copyright 2002
American Mathematical Society