Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 693-735

LINEAR DIFFERENTIAL POLYNOMIALS IN ZERO-FREE MEROMORPHIC FUNCTIONS

James K. Langley

University of Nottingham, School of Mathematical Sciences
NG7 2RD, United Kingdom; james.langley 'at' nottingham.ac.uk

Abstract. The paper determines all meromorphic functions f in C such that f and F have finitely many zeros, where F = f^(k) + a_k–1f^(k–1) + ... + a₀f with k ≥ 3 and the a_j rational functions.

2010 Mathematics Subject Classification: Primary 30D35.

Key words: Meromorphic function, zeros.

Reference to this article: J. K. Langley: Linear differential polynomials in zero-free meromorphic functions. Ann. Acad. Sci. Fenn. Math. 43 (2018), 693-735.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4348