On the number of zeros of certain rational harmonic functions

被引：57

作者：

Khavinson, D ^{[1
]}

Neumann, G

机构：

[1] Univ Arkansas, Dept Math Sci, Fayetteville, AR 72701 USA

[2] Kansas State Univ, Dept Math, Manhattan, KS 66506 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2006年 / 134卷 / 04期

关键词：

Argument principle; Fixed points; Gravitational lenses; Rational harmonic mappings;

D O I：

10.1090/S0002-9939-05-08058-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Extending a result of Khavinson and Swiatek (2003) we show that the rational harmonic function <(r(z))over bar > - z, where r(z) is a rational function of degree n > 1, has no more than 5n - 5 complex zeros. Applications to gravitational lensing are discussed. In particular, this result settles a conjecture by Rhie concerning the maximum number of lensed images due to an n-point gravitational lens.

引用

页码：1077 / 1085

页数：9

共 21 条

[1]

Bshouty D., 2004, Comput. Methods Funct. Theory, V4, P35, DOI DOI 10.1007/BF03321053

[2]

BURKE WL, 1981, ASTROPHYS J, V244, pL1, DOI 10.1086/183466

[3]

Carleson L, 1993, COMPLEX DYNAMICS

[4]

DAVIS PJ, 1974, SCHWARZ FUNCTION APP

[5]

FORSTER O, 1981, LECT RIEMANN SURFACE, P81

[6]

GEYER L, 2003, SHARP BOUNDS VALENCE

[7] On the number of zeros of certain harmonic polynomials [J].

Khavinson, D ;

Swiatek, G .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 131 (02) :409-414

[8]

MAO S, 1997, P 8 MARC GROSSM M GE

[9]

NARAYAN R, 1995, P 1995 JER WINT SCH

[10]

*NASA, 2001, GIANT CLUST BENDS BR

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