ON THE ZEROS OF MEROMORPHIC FUNCTIONS OF THE FORM F(Z)=SIGMA(K=1)INFINITY A(K)/Z-Z(K)

被引：30

作者：

EREMENKO, A

LANGLEY, J

ROSSI, J

机构：

[1] UNIV NOTTINGHAM,DEPT MATH,NOTTINGHAM NG7 2RD,ENGLAND

[2] VIRGINIA POLYTECH INST & STATE UNIV,DEPT MATH,BLACKSBURG,VA 24061

[3] UNIV ILLINOIS,CHICAGO,IL 60680

[4] YORK UNIV,YORK,N YORKSHIRE,ENGLAND

来源：

JOURNAL D ANALYSE MATHEMATIQUE | 1994年 / 62卷

关键词：

D O I：

10.1007/BF02835958

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the zero distribution of meromorphic functions of the form f(z) = Sigma(k=1)(infinity) a(k)/z-z(k) where a(k) > 0. Noting that f is the complex conjugate of the gradient of a logarithmic potential, our results have application in the study of the equilibrium points of such a potential. Furthermore, answering a question of Hayman, we also show that the derivative of a meromorphic function of order at most one, minimal type has infinitely many zeros.

引用

页码：271 / 286

页数：16

共 15 条

[1]

ANDERSON RD, 1983, ECON HIST REV, V36, P518

[2]

CLUNIE J, IN PRESS J LONDON MA

[3] CONVOLUTION INEQUALITIES, REGULAR VARIATION AND EXCEPTIONAL SETS [J].

DRASIN, D ;

SHEA, DF .

JOURNAL D ANALYSE MATHEMATIQUE, 1976, 29 :232-293

[4]

EREMENKO M, 1990, SOV MATH, V48, P386

[5]

Goldberg A. A., 2008, VALUE DISTRIBUTION M

[6]

Hayman W. K., 1976, SUBHARMONIC FUNCTION, VI

[7]

Hayman W. K., 1964, MEROMORPHIC FUNCTION

[8]

Hayman W.K., 1989, SUBHARMONIC FUNCTION, V2

[9]

Hayman W.K., 1958, MULTIVALENT FUNCTION

[10] ON THE GROWTH OF SOLUTIONS OF F'' + GF' + HF = 0 [J].

HELLERSTEIN, S ;

MILES, J ;

ROSSI, J .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 324 (02) :693-706

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