Zeros and poles of meromorphic functions

2000 ◽  
pp. 83-89
Author(s):  
Peter Kravanja ◽  
Marc Van Barel
Keyword(s):  
Meromorphic Functions ◽  
Zeros And Poles

Meromorphic functions with prescribed asymptotic behaviour, zeros and poles and applications in complex approximation

1999 ◽  
Vol 51 (1) ◽  
pp. 117-129
Author(s):  
A. Sauer
Keyword(s):  
Power Series ◽  
Asymptotic Behaviour ◽  
Series Expansion ◽  
Meromorphic Functions ◽  
Power Series Expansion ◽  
Complex Approximation ◽  
Asymptotic Power ◽  
Approximation Theorems ◽  
Zeros And Poles

AbstractWe construct meromorphic functions with asymptotic power series expansion in z−1 at ∞ on an Arakelyan set A having prescribed zeros and poles outside A. We use our results to prove approximation theorems where the approximating function fulfills interpolation restrictions outside the set of approximation.

Meromorphic Functions Sharing the Same Zeros and Poles

2004 ◽  
Vol 56 (6) ◽  
pp. 1190-1227 ◽  
Author(s):  
Günter Frank ◽  
Xinhou Hua ◽  
Rémi Vaillancourt
Keyword(s):  
Meromorphic Function ◽  
Meromorphic Functions ◽  
Zeros And Poles

AbstractIn this paper, Hinkkanen's problem (1984) is completely solved, i.e., it is shown that any meromorphic function f is determined by its zeros and poles and the zeros of f(j) for j = 1, 2, 3, 4.

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