Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-23T19:20:51.884Z Has data issue: false hasContentIssue false
  • English
  • Français

Integer Points of Meromorphic Functions

Published online by Cambridge University Press:  21 August 2013

Matthew Buck
Matthew Buck*
Affiliation:
School of Mathematical Sciences, University Park, University of Nottingham, Nottingham NG7 2RD, UK, ([email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Working from a half-plane result of Fletcher and Langley, we show that if f is an integer-valued function on some subset of the natural numbers of positive lower density and is meromorphic of sufficiently small exponential type in the plane, then f is a polynomial.

Keywords

integer-valued functionsmeromorphic functionsNevanlinna theoryvalue distributionPrimary 30D3030D35
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 2 , June 2014 , pp. 367 - 376
Copyright
Copyright © Edinburgh Mathematical Society 2014 

References

1.Buck, R. C., Integral-valued entire functions, Duke Math. J. 15 (1948), 879–891.Google Scholar
2.Fletcher, A. N., Gaussian integer points of functions analytic in a half-plane, Proc. Camb. Phil. Soc. 145 (2008), 257–272.Google Scholar
3.Fletcher, A. N. and Langley, J. K., Integer points of analytic functions in a half-plane, Proc. Edinb. Math. Soc. 52 (2009), 619–630.Google Scholar
4.Hayman, W. K., Meromorphic functions (Clarendon, Oxford, 1964).Google Scholar
5.Hayman, W. K., Subharmonic functions, Volume 2 (Academic, 1989).Google Scholar
6.Laine, I., Complex analysis 2 (available at www.joensuu.fi/matematiikka/kurssit/complex/).Google Scholar
7.Langley, J. K., Integer points of entire functions, Bull. Lond. Math. Soc. 38 (2006), 239–249.Google Scholar
8.Langley, J. K., Integer-valued analytic functions in a half-plane, Computat. Meth. Funct. Theory 7 (2007), 433–442.Google Scholar
9.Pisot, C., Über ganzwertige ganze Funktionen, Jahresber. Dtsch. Math.-Verein. 52 (1942), 95–102.Google Scholar
10.Pólya, G., Über ganze ganzwertige Funktionen, Rend. Circ. Mat. Palermo 40 (1915), 1–16.CrossRefGoogle Scholar
11.Robinson, R. M., Integer-valued entire functions, Trans. Am. Math. Soc. 153 (1971), 451–468.Google Scholar
12.Selberg, A., Über ganzwertige ganze transzendente Funktionen, Arch. Mat. Natur. 44 (1941), 45–52.Google Scholar
13.Waldschmidt, M., Integer-valued entire functions on Cartesian products, in Number theory in progress, Volume 1, pp. 553–576 (Walter de Gruyter, Berlin, 1999).Google Scholar
14.Yoshino, K., Polya's theorem for non-entire functions, Rend. Circ. Mat. Palermo 3 (1984), 385–395.Google Scholar