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Jim Langley

Professor of Mathematics, Faculty of Science

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Research Summary

Jim Langley works on concrete problems in complex analysis, mainly linked to Nevanlinna theory, with some applications to differential equations and complex dynamics (iteration). Professor Langley… read more

Recent Publications

Current Research

Jim Langley works on concrete problems in complex analysis, mainly linked to Nevanlinna theory, with some applications to differential equations and complex dynamics (iteration). Professor Langley has supervised ten PhD students to date, and the main themes of his research are the following. * Zeros of derivatives. There is a long history of work on these questions which can be viewed as natural generalizations of the classical Picard theorem to the effect that an entire function which omits two values is a constant. Langley's best known result is probably his 1993 proof of Hayman's 1959 conjecture on the zeros of a meromorphic function and its second derivative. More recently, Langley, Bergweiler and Eremenko settled the last remaining case of a famous conjecture of Wiman from 1911 concerning the derivatives of real entire functions, and in recent years Langley has mainly been working on non-real zeros of derivatives of meromorphic functions. * Differential equations in the complex domain, in particular the growth and oscillation of solutions of linear differential equations. * Properties of compositions of entire functions. This area has connections to complex dynamics, in which the famous Julia and Mandelbrot sets arise, and which has been a very successful field of research in recent years. * Critical points of potentials associated with distributions of charged points and wires, and zeros of related meromorphic functions.

  • LANGLEY, J.K., 2017. Trajectories escaping to infinity in finite time Proceedings of the American Mathematical Society. 145, 2107-2117
  • LANGLEY, J.K., 2017. Non-real zeros of derivatives of meromorphic functions Journal d'Analyse Mathematique. 133(1), 183-228
  • LANGLEY, J.K., 2017. Linear differential polynomials in zero-free meromorphic functions Annales Academiæ Scientiarum Fennicæ Mathematica. (In Press.)
  • LANGLEY, J. K., 2016. The Schwarzian derivative and the Wiman-Valiron property JOURNAL D ANALYSE MATHEMATIQUE. 130, 71-89
  • J.K. LANGLEY, 2014. Derivatives of meromorphic functions of finite order Computational Methods and Function Theory. 14(2-3), 195-207
  • J.K. LANGLEY and JOHN ROSSI, 2014. Wiman-Valiron theory for a class of functions meromorphic in the unit disc Mathematical Proceedings of the Royal Irish Academy. 114A(2), 137-148
  • J.K. LANGLEY, 2013. Second order linear differential polynomials and real meromorphic functions Results in Mathematics. 63, 151-169
  • LANGLEY and ABDULLAH ALOTAIBI, 2013. The separation of zeros of solutions of higher order linear differential equations with entire coefficients Results in Mathematics. 63, 1365-1373
  • J.K. LANGLEY, 2013. The reciprocal of a real entire function and non-real zeros of higher derivatives Annales Academiæ Scientiarum Fennicæ: Mathematica. 38, 855-871
  • J.K. LANGLEY, 2012. Zeros of Derivatives of Real Meromorphic Functions Computational Methods and Function Theory. 12, 241-256
  • LANGLEY, J.K., 2011. Value distribution of differences of meromorphic functions Rocky Mountain Journal of Mathematics. 41, 275-291 (In Press.)
  • LANGLEY, J., 2011. Zeros of derivatives of meromorphic functions Computational Methods and Function Theory. 10(2), 421-439
  • LANGLEY, J.K., 2011. Non-real zeros of derivatives of real meromorphic functions of infinite order Mathematical Proceedings of the Cambridge Philosophical Society. 150(2), 343-351
  • LANGLEY, JK, 2011. Non-Real Zeros Of Real Differential Polynomials Proceedings Of The Royal Society Of Edinburgh Section A-Mathematics. 141, 631-639
  • JAMES K LANGLEY, 2011. An inequality of Frank, Steinmetz and Weissenborn Kodai Mathematical Journal. 34(3), 383-389
  • ALOTAIBI, A. and LANGLEY, J. K., 2010. On solutions of linear differential equations with entire coefficients Journal of Mathematical Analysis and Applications. VOL 367(NUMBER 2), 451-460
  • LANGLEY, J.K., 2010. Real meromorphic functions and linear differential polynomials Science China (Mathematics). 53(3), 739-748
  • BERGWEILER, W., FLETCHER, A., LANGLEY, J. and MEYER, J., 2009. The escaping set of a quasiregular mapping Proceedings of the American Mathematical Society. 137, 641-651
  • FLETCHER, A., LANGLEY, J.K. and MEYER, J., 2009. Slowly growing meromorphic functions and the zeros of differences Mathematical Proceedings of the Royal Irish Academy. VOL 109(NUMB 2), 147-154
  • FLETCHER, A.N. and LANGLEY, J.K., 2009. Meromorphic compositions and target functions Annales Academiae Scientiarum Fennicae. Series A. I: Mathematica. VOL 34(PART 2), 615-636
  • FLETCHER, A., LANGLEY, J.K. and MEYER, J., 2009. Nonvanishing derivatives and the MacLane class A Illinois Journal of Mathematics. 53, 379-390
  • LANGLEY, J.K., 2009. Non-real zeros of linear differential polynomials Journal d'Analyse Mathématique. 107(1), 107-140
  • LANGLEY, J.K., 2009. Logarithmic Singularities and the Zeros of the Second Derivative Computational Methods and Function Theory. VOL 9(NUMB 2), 565-578
  • LANGLEY, J.K., 2009. Non-real zeros of derivatives of real meromorphic functions Proceedings of the American Mathematical Society. VOL 137(NUMB 10), 3355-3368
  • LANGLEY, J.K. and MEYER, J., 2009. A Generalisation of the Bank-Laine Property Computational Methods and Function Theory. VOL 9(NUMB 1), 213-226
  • FLETCHER, A. and LANGLEY, J.K., 2009. Integer points of analytic functions in a half-plane Proceedings of the Edinburgh Mathematical Society. 52, 631-651
  • DRASIN, D. and LANGLEY, J.K., 2008. Bank-Laine functions via quasiconformal surgery. In: RIPPON, P.J. and STALLARD, G.M., eds., Transcendental dynamics and complex analysis: London Mathematical Society Lecture Note Series 348 Cambridge University Press. 165-178
  • ALOTAIBI, A. and LANGLEY, J.K., 2008. The zeros of certain differential polynomials Analysis. 28, 269-282
  • LANGLEY, J.K., 2008. Meromorphic Functions in the Class S and the Zeros of the Second Derivative COMPUTATIONAL METHODS AND FUNCTION THEORY. VOL 8(NUMB 1/2), 73-84
  • EREMENKO, A and LANGLEY, J.K., 2008. Appendix B. A survey of some results after 1970. In: OSTROVSKII, MIKHAIL (TRANSLATOR), ed., Value distribution of meromorphic functions, by A.A. Gol'dberg and I.V. Ostrovskii American Mathematical Society.
  • LANGLEY, J., 2007. Integer-Valued Analytic Functions in a Half-Plane COMPUTATIONAL METHODS AND FUNCTION THEORY. VOL 7(NUMB 2), 433-442
  • LANGLEY, J.K. and LINGHAM, E.F., 2007. On the derivatives of composite functions New Zealand Journal of Mathematics. 36, 57-61
  • BERGWEILER, W., DRASIN, D. and LANGLEY, J. K., 2007. Baker domains for Newton's method ANNALES- INSTITUT FOURIER. VOL 57(PART 3), 803-814
  • LANGLEY, J. K., 2007. Zeros of Meromorphic Functions with Poles Close to the Real Axis RESULTS IN MATHEMATICS. VOL 51(NUMBER 1-2), 87-96
  • LANGLEY, J. K., 2007. Equilibrium points of logarithmic potentials on convex domains PROCEEDINGS- AMERICAN MATHEMATICAL SOCIETY. VOL 135(NUMB 9), 2821-2826
  • BERGWEILER, W. and LANGLEY, J. K., 2007. Zeros of differences of meromorphic functions MATHEMATICAL PROCEEDINGS - CAMBRIDGE PHILOSOPHICAL SOCIETY. VOL 142(PART 1), 133-148
  • LANGLEY, J.K., 2006. Integer points of entire functions Bulletin of the London Mathematical Society. 38(2), 239-249
  • LANGLEY, J. K., 2006. Pairs of non-homogeneous linear differential polynomials PROCEEDINGS- ROYAL SOCIETY OF EDINBURGH A. VOL 136(PART 4), 785-794
  • LANGLEY, J., 2006. Solution of a Problem of Edwards and Hellerstein COMPUTATIONAL METHODS AND FUNCTION THEORY. VOL 6(NUMB 1), 243-252
  • LANGLEY, J.K., 2005. Non-real zeros of higher derivatives of real entire functions of infinite order Journal d'Analyse Mathématique. 97, 357-396
  • BERGWEILER, W., EREMENKO, A. and LANGLEY, J. K., 2005. Zeros of differential polynomials in real meromorphic functions Edinburgh Mathematical Society. Proceedings. VOL 48(PART 2), 279-294
  • LANGLEY, J. K., 2005. Integer Points of Meromorphic Functions Computational Methods and Function Theory. VOL 5(NUMB 2), 253-262
  • LANGLEY,J.K. and ELZAIDI,S.M., 2005. Bank-Laine functions with periodic zero-sequences Resultate der Mathematik. 48, 34-43
  • BERGWEILER, W. and LANGLEY, J. K., 2005. Multiplicities in Hayman's alternative Journal of the Australian Mathematical Society. VOL 78(PART 1), 37-58
  • LANGLEY, J. K. and ROSSI, J., 2004. Meromorphic functions of the form f(z) = Sigma~n~=~1 a~n/(z - z~n) Revista Matematica Iberoamericana. VOL 20(NUMB 1), 285-314
  • LANGLEY, J. K. and ROSSI, J., 2004. Critical Points of Certain Discrete Potentials Complex Variables: Theory and Application. VOL 49(PART 7/9), 621-638
  • LANGLEY, J. K., 2004. Deficient Values of Derivatives of Meromorphic Functions in the Class S Computational Methods and Function Theory. VOL 4(NUMB 1), 237-247
  • LANGLEY, J.K., 2004. The work of Ilpo Laine on complex differential equations. In: Symposium on Complex Differential and Functional Equations, 9--19, Univ. Joensuu Dept. Math. Rep. Ser., 6.
  • BERGWEILER, W., EREMENKO, A. and LANGLEY, J.K., 2003. Real entire functions of infinite order and a conjecture of Wiman Geometric and Functional Analysis. 13(5), 975-991
  • LANGLEY, J.K., 2003. The second derivative of a meromorphic function of finite order Bulletin of the London Mathematical Society. 35(1), 97-108
  • LANGLEY,J.K. and BERGWEILER,W., 2003. Nonvanishing derivatives and normal families Journal d'Analyse Mathématique. 91, 353-367
  • LANGLEY, J. K., 2003. The zeros of ff"- b RESULTS IN MATHEMATICS. VOL 44(PART 1/2), 130-140
  • LANGLEY, J. K., 2002. Composite Bank-Laine functions and a question of Rubel Transactions of the American Mathematical Society. VOL 354(PART 3), 1177-1192
  • LANGLEY, J. K., 2002. Linear differential equations with entire coefficients of small growth Archiv der Mathematik. VOL 78(PART 4), 291-296
  • LANGLEY, J. K., 2002. Critical Values of Slowly Growing Meromorphic Functions Computational Methods and Function Theory. VOL 2(NUMB 2), 539-548
  • LANGLEY, J. K., 2002. The distribution of finite values of meromorphic functions with deficient poles Mathematical Proceedings of the Cambridge Philosophical Society. VOL 132(PART 2), 311-318
  • LANGLEY, J. K., 2001. The second derivative of a meromorphic function Edinburgh Mathematical Society. Proceedings. VOL 44(PART 3), 455-478
  • LANGLEY, J. K., 2001. Bank-Laine functions with sparse zeros Proceedings of the American Mathematical Society. VOL 129(PART 7), 1969-1978
  • LANGLEY, J. K., 2000. A Certain Functional-Differential Equation Journal of Mathematical Analysis and Applications. VOL 244(PART 2), 564-567
  • LANGLEY,J.K. and FRANK,G., 1999. Pairs of linear differential polynomials Analysis. 19, 173-194
  • LANGLEY, J. K., 1999. Complex Oscillation and Removable Sets Journal of Mathematical Analysis and Applications. VOL 235(NUMBER 1), 227-236
  • FRANK, G. and LANGLEY, J. K., 1999. On the zeros of pairs of linear differential polynomials Annales Academiae Scientiarum Fennicae. Series A. I: Mathematica. VOL 24(NUMBER 2), 409-436
  • LANGLEY, J. K., 1999. Permutable entire functions and Baker domains Mathematical Proceedings of the Cambridge Philosophical Society. VOL 125(NUMBER 2), 199-202
  • LANGLEY, J. K., 1999. On differential polynomials, fixpoints and critical values of meromorphic functions Resultate der Mathematik. VOL 35(NUMBER 3/4), 284-309
  • LANGLEY, J. K. and ZHENG, J. H., 1998. On the fixpoints, multipliers and value distribution of certain classes of meromorphic functions Annales Academiae Scientiarum Fennicae. Series A. I: Mathematica. VOL 23(NUMBER 1), 133-150
  • LANGLEY, J. K., 1998. On the Zeros of f^(^k^)/f Complex Variables: Theory and Application. VOL 37(NUMBER 1/4), 385-394
  • SHEA,D. and LANGLEY,J.K., 1998. On multiple points of meromorphic functions Journal of the London Mathematical Society. 57, 371-384
  • LANGLEY, J. K., 1998. Quasiconformal modifications and Bank-Laine functions Archiv der Mathematik. VOL 71(NUMBER 3), 233-239
  • KAUFMAN, R. and LANGLEY, J., 1997. Steven Barry Bank 1939-1994 Complex Variables: Theory and Application. VOL 34(NUMBER 1/2), 1-6
  • LANGLEY, J. K., 1997. On the zeros of the second derivative Royal Society of Edinburgh. Proceedings. Section A (Mathematics). VOL 127(NUMBER 2), 359-368
  • DRASIN, D. and LANGLEY, J. K., 1997. On Deficiencies and Fixpoints of Composite Meromorphic Functions Complex Variables: Theory and Application. VOL 34(NUMBER 1/2), 63-82
  • LANGLEY, J.K., 1996. Two results related to a question of Hinkkanen Kodai Mathematical Journal. 19, 52-61 (In Press.)
  • LANGLEY, J. K., 1996. The zeros of the first two derivatives of a meromorphic function Proceedings of the American Mathematical Society. VOL 124(NUMBER 8), 2439-2442
  • LANGLEY, J. K., 1996. A lower bound for the number of zeros of a meromorphic function and its second derivative Edinburgh Mathematical Society. Proceedings. VOL 39(NUMBER 1), 171-185
  • LANGLEY, J.K., 1996. The zeros of the second derivative of a meromorphic function In: XVIth Rolf Nevanlinna Colloquium. 101-109
  • LANGLEY, J.K., 1996. On the zeros of solutions of certain linear differential equations Resultate der Mathematik. 29, 276-279 (In Press.)
  • LANGLEY, J.K., 1995. On entire solutions of linear differential equations with one dominant coefficient Analysis. 15, 187-204 (In Press.)
  • LANGLEY, J.K., 1995. On the multiple points of certain meromorphic functions Proceedings of the American Mathematical Society. 123, 1787-1795 (In Press.)
  • BERGWEILER, WALTER, CLUNIE, JIM and LANGLEY, JIM, 1995. Proof of a conjecture of Baker concerning the distribution of fixpoints Bulletin of the London Mathematical Society. 27, 148-154 (In Press.)
  • LANGLEY, J.K., 1994. On linear differential equations and gap series Complex Variables: Theory and Application. 24, 59-66 (In Press.)
  • LANGLEY, J.K., 1994. On second order linear differential polynomials Resultate der Mathematik. 26, 51-82 (In Press.)
  • EREMENKO, ALEXANDRE, LANGLEY, JIM and ROSSI, JOHN, 1994. On the zeros of meromorphic functions of the form sum_{k=1}^infty a_k/(z-z_k) Journal d'Analyse Mathématique. 62, 271-286 (In Press.)
  • LANGLEY, J.K., 1994. On the fixpoints of composite entire functions of finite order Proceedings of the Royal Society of Edinburgh A. 124, 995-1001 (In Press.)
  • LANGLEY, J.K., 1993. Proof of a conjecture of Hayman concerning f and f'' Journal of the London Mathematical Society. 48, 500-514 (In Press.)
  • LANGLEY, J.K., 1992. On the deficiencies of composite entire functions Proceedings of the Edinburgh Mathematical Society. 36, 151-164 (In Press.)

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