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Zeros of Derivatives of Real Meromorphic Functions

Zeros of Derivatives of Real Meromorphic Functions Two results are proved for real meromorphic functions in the plane. First, a lower bound is given for the distance between distinct non-real poles when the function and its second derivative have finitely many non-real zeros and the logarithmic derivative has finite lower order. Second, if the function has finitely many non-real zeros, and one of its higher derivatives has finitely many zeros in the plane, and if the multiplicities of non-real poles grow sufficiently slowly, then the function is a rational function multiplied by the exponential of a polynomial. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Zeros of Derivatives of Real Meromorphic Functions

Computational Methods and Function Theory , Volume 12 (1) – Jan 25, 2012

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Publisher
Springer Journals
Copyright
Copyright © 2012 by Heldermann  Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321825
Publisher site
See Article on Publisher Site

Abstract

Two results are proved for real meromorphic functions in the plane. First, a lower bound is given for the distance between distinct non-real poles when the function and its second derivative have finitely many non-real zeros and the logarithmic derivative has finite lower order. Second, if the function has finitely many non-real zeros, and one of its higher derivatives has finitely many zeros in the plane, and if the multiplicities of non-real poles grow sufficiently slowly, then the function is a rational function multiplied by the exponential of a polynomial.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Jan 25, 2012

References