Prof. J.K. Langley, School of Mathematical Sciences, University of Nottingham, NG7 2RD.

  • back to Jim Langley's home page


    My research is on the value distribution of meromorphic functions, with particular reference to zeros of derivatives, and occasionally to iteration and to differential equations in the complex domain.

    Here are PDF versions of some recent talks I have given:

  • Bank-Laine functions and complex DEs (various seminars 1998-99)
  • Meromorphic functions and their derivatives (British Mathematical Colloquium 1997)
  • Second order differential equations and a question of Rubel concerning asymptotic paths (Function Theory and Function Spaces Meeting, Nottingham, September 2000).
  • A question of Rubel concerning asymptotic paths (IC, October 2000)
  • QC surgery and critical points of certain potentials (Warwick 2001)
  • Nichtreelle Nullstellen der Ableitungen ganzer Funktionen (TU Berlin 2005)
  • Integer points of entire functions (CMFT and One Day Function Theory Meeting 2005)
  • Equilibrium points of logarithmic potentials on convex domains (Tag der Funktionentheorie, Aachen, June 2006)
  • Zeros of derivatives in the plane and off the real line (Paris-London Analysis Seminar, October 2009: a similar talk given at CMFT, Ankara, June 2009)
  • Non-real zeros of derivatives of real meromorphic functions (Oktoberfest, Cardiff 2010)
  • Integer points of entire functions (Frontiers of Nevanlinna Theory I, London March 2011)
  • An introduction to Nevanlinna theory (ICMS Workshop on The role of complex analysis in complex dynamics, Edinburgh, May 2013)

    A lot of these talks concern the former Wiman conjecture, for which more details can be found below:

  • The former Wiman conjecture: some background
  • More remarks on the former Wiman conjecture

    Some numerical investigations by Fangzhao Liu, supported by a grant from the Nuffield Foundation, can be found here:

  • Numerical investigations related to problems in mathematical analysis

    You can also read a brief introduction to some of my research from ca. 2002 in

  • PDF file jklresearch.pdf

    and a description of some of my research ca. 2007 in

  • PDF file

    My postgraduate notes are in PDF: postgraduate notes

    You can find a list of my publications, in some cases with dvi and/or PDF files, at

  • Jim Langley's publications

    Here is a photo from the 2012 One Day Function Theory Meeting:

    Poem by Wolfgang Fuchs: Oberwolfach 1986

    Here are some links to some function theory pages and other useful sources:

  • Alex Eremenko's home page
  • Walter Bergweiler's home page
  • Norbert Steinmetz' home page
  • Katsuya Ishizaki's home page
  • The Finnish Annals
  • XXX archive
  • MathSciNet
  • Mandelbrot and Julia set explorer
  • The Mandelbrot /Julia set Applet
  • Goettingen archive
  • Goettingen archive (search)

    Measure and Integration notes: my notes for this former module (no longer taught at Nottingham) are viewable in a PDF version.

    Here are some further notes on measure theory, again viewable in a PDF version.

    first year Real Analysis: I taught first year Real Analysis for many years and my lecture notes (from a long-discontinued module) are available here in

  • PDF format .
    Note that not all pdf viewers will display these notes correctly, but they seem to be fine with Adobe Acrobat (e.g. on Windows IE).

    All these notes are Copyright © J.K. Langley, but freely available for personal use.