On the number of zeros of certain functions
نویسندگان
چکیده
منابع مشابه
On the Number of Zeros of Certain Rational Harmonic Functions
Extending a result of Khavinson and Świa̧tek (2003) we show that the rational harmonic function r(z) − 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.
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where J and N are positive integers, and the X's are real or complex constants. It is assumed that we do not have XON = XiN = .. = XJN, and that we do not have XOn = Xln = . . . = )kXj * Ofor any n < N. It is also assumed that no two terms in the right-hand member of (1) are identical or differ only by a constant factor. The work reported here is essentially a generalization, in one direction, ...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae (Proceedings)
سال: 1975
ISSN: 1385-7258
DOI: 10.1016/1385-7258(75)90049-9