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Author:
P. C. Fenton

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

MSC (2000):
Primary 30D15

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 𝑐𝑜𝑠𝜋𝜌 theorem*, Trans. Amer. Math. Soc.**193**(1974), 181–197. MR**0344468**, 10.1090/S0002-9947-1974-0344468-7**2.**Ralph Philip Boas Jr.,*Entire functions*, Academic Press Inc., New York, 1954. MR**0068627****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. Appl.**244**(2000), no. 1, 214–222. MR**1746798**, 10.1006/jmaa.1999.6702**5.**Bo Kjellberg,*On the minimum modulus of entire functions of lower order less than one*, Math. Scand.**8**(1960), 189–197. MR**0125967****6.**Bo Kjellberg,*A theorem on the minimum modulus of entire functions*, Math. Scand.**12**(1963), 5–11. MR**0159942**

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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