Professor

Biography

Prof. Chiang attended several primary and secondary schools in Hong Kong before he received both his undergraduate (1984) and postgraduate (1991) qualification from University College London. His PhD was directed under the late Professor J. Milne Anderson on topics related to Schwarzian derivatives and linear differential equations. Although special functions are almost as old as calculus, many of the centuries old special functions that appear frequently in applications are still far from being understood. His current interests lie in application of Nevanlinna theory, algebraic and geometric methods to better understand these special functions.

Research Interests

Complex function theory; ordinary differential equations in the complex plane; orthogonal polynomials; difference equations

Selected Publications

  Article

1. Wiman-Valiron theory of a polynomial series based on Askey-Wilson divided difference operator
   • Author(s): Cheng, Kam Hang; Chiang, Yik Man
   • Source: Constructive Approximation, 12 March 2021
   • Year: 2021


2. Resolving Singularities and Monodromy Reduction of Fuchsian Connections
   • Author(s): Chiang, Yik Man; Ching, Avery; Tsang, Chin-Yin
   • Source: Annales Henri Poincaré, 27 April 2021
   • Year: 2021


3. Galoisian approach to complex oscillation theory of some Hill equations
   • Author(s): Chiang, Yik Man ; Yu, GUO-FU
   • Source: Mathematica Scandinavica, v. 124, (1), January 2019, p. 102-131
   • Year: 2019


4. Symmetry of the Darboux equation
   • Author(s): Chiang, Yik Man ; Tsang, Chiu Yin ; Ching, Avery
   • Source: Kumamoto Journal of Mathematics. , v. 31, January 2018, p. 15-48
   • Year: 2018


5. Nevanlinna Theory of the Askey–wilson Divided Difference Operator
   • Author(s): Chiang, Yik Man ; Feng, shaoji
   • Source: Advances in Mathematics. , v. 329, April 2018, p. 217-272
   • Year: 2018


6. Difference Nevanlinna Theories With Vanishing and Infinite Periods
   • Author(s): Chiang, Yik Man; Luo, Xudan
   • Source: Michigan Mathematical Journal. , v. 66, (3), 2017, p. 451-480
   • Year: 2017


7. Nevanlinna Theory of the Wilson Divided-difference Operator
   • Author(s): Cheng, Kam Hang; Chiang, Yik-Man
   • Source: Annales Academiae Scientiarum Fennicae Mathematica. , v. 42, (1), 2017, p. 175-209
   • Year: 2017


8. On the Growth of Logarithmic Difference of Meromorphic Functions and a Wiman–Valiron Estimate
   • Author(s): Chiang, Yik Man; Feng, Shao-Ji
   • Source: Constructive Approximation. , v. 44, (3), December 2016, p. 313-326
   • Year: 2016


9. On complex oscillation, function-theoretic quantization of non-homogeneous periodic ordinary differential equations and special functions
   • Author(s): Chiang, Yik Man ; Yu, Kit Wing
   • Source: Proceedings of the Royal Society of Edinburgh Section A: Mathematics. , v. 142A, (3), June 2012, p. 449-477
   • Year: 2012


10. Subnormal solutions of non-homogeneous periodic ODEs, special functions and related polynomials
    • Author(s): Chiang, Yik-Man; Yu, Kit-Wing
    • Source: Journal für die reine und angewandte Mathematik. , v. 651, February 2011, p. 127-164
    • Year: 2011


11. On the Growth of Logarithmic Differences, Difference Quotients and Logarithmic Derivatives of Meromorphic Functions
    • Author(s): Chiang, Yik-Man; Feng, Shao-Ji
    • Source: Transactions of the American Mathematical Society. , v. 361, (7), 2009, JUL, p. 3767-3791
    • Year: 2009


12. On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane
    • Author(s): Chiang, Yik-Man; Feng, Shao-Ji
    • Source: The Ramanujan Journal. , v.16, (1), 2008, MAY, p. 105-129
    • Year: 2008


13. Difference independence of the Riemann zeta function
    • Author(s): Chiang, Yik-Man; Feng, Shao-Ji
    • Source: Acta Arithmetica. , v. 125, (4), 2006, p. 317-329
    • Year: 2006


14. On value distribution theory of second order periodic ODEs, special functions and orthogonal polynomials
    • Author(s): Chiang, Yik-Man; Ismail, Mourad E.H.
    • Source: CANADIAN journal OF mathematics-journal canadien DE Mathematiques. , v. 58, (4), 2006, AUG, p. 726-767
    • Year: 2006


15. On the nevanlinna order of meromorphic solutions to linear analytic difference equations
    • Author(s): Chiang, YM; Ruijsenaars, SNM
    • Source: Studies in applied mathematics. , v. 116, (3), 2006, APR, p. 257-287
    • Year: 2006


16. Estimates on the growth of meromorphic solutions of linear differential equations
    • Author(s): Chiang, YM; Hayman, WK
    • Source: Commentarii mathematici Helvetici. , v. 79, (3), 2004, SEP, p. 451-470
    • Year: 2004


17. On the meromorphic solutions of an equation of Hayman
    • Author(s): Chiang, YM; Halburd, RG
    • Source: Journal of mathematical analysis and applications. , v. 281, (2), 2003, MAY 15, p. 663-677
    • Year: 2003


18. On a problem in complex oscillation theory of periodic second order linear differential equations and some related perturbation results
    • Author(s): Chiang, YM; Gao, SA
    • Source: ANNALES Academiae scientiarum fennicae-mathematica. , v. 27, (2), 2002, p. 273-290
    • Year: 2002


19. Complex oscillation theory and special functions
    • Author(s): Chiang, Yik-Man; Ismail, M.E.H.
    • Source: Mathematical Reports of the Academy of Science of Canada. , Vol. 24, pp. 117-123
    • Year: 2002


20. On the zero-free solutions of linear periodic differential equations in the complex plane
    • Author(s): Chiang, Yik Man
    • Source: Results in Mathematics. , v. 38, (3-4), November 2000, p. 213-225
    • Year: 2000


21. Some oscillation results for linear differential equations in the complex plane
    • Author(s): Chiang, Yik Man ; Laine, Ilpo
    • Source: Japanese Journal of Mathematics. , v. 24, (2), 1998, p. 367-402
    • Year: 1998


22. Oscillation results of certain higher order linear differential equations with periodic coefficients in the complex plane
    • Author(s): Chiang, YM; Wang, SP
    • Source: Journal of mathematical analysis and applications. , v. 215, (2), 1997, NOV 15, p. 560-576
    • Year: 1997


23. Oscillation results on y″ + Ay = 0 in the complex domain with transcendental entire coefficients which have extremal deficiencies
    • Author(s): Chiang, Yik Man
    • Source: Proceedings of the Edinburgh Mathematical Society, v. 38, (1), February 1995, p. 13-34
    • Year: 1995


24. On the complex oscillation of y′′ + (ez − K)y = 0 and a result of Bank
    • Author(s): Chiang, Y.M.
    • Source: Laine and Langley, Proc. Comput. Methods and Function Theory, Series in Approximations and Decompositions. , v. 5, 1995, p. 125-134
    • Year: 1995


25. Oscillation results for some linear differential equations
    • Author(s): Chiang, YM; Laine, I.; Wang, SP
    • Source: Mathematica Scandinavica. , v. 77, (2), 1995, p. 209-224
    • Year: 1995


26. Oscillation results on y "+ Ay= 0 in the complex domain with transcendental entire coefficients which have extremal deficiencies
    • Author(s): Chiang, YM
    • Source: Proceedings of the Edinburgh Mathematical Society. , v. 38, (1), p. 13-34
    • Year: 1995


27. Some properties of analytic functions with small schwarzian
    • Author(s): Chiang, Y.M.
    • Source: Complex Variables Theory and Application. , . 25, 1994, p. 107-118
    • Year: 1994


28. Some remarks on Lehto's domain constant
    • Author(s): Chiang, Y.M.
    • Source: Annales Academiae Scientiarum Fennicae. Series A I. Mathematica. , . 17, 1992, p. 285-293
    • Year: 1992


29. On a subclass of strongly gamma-starlike functions and quasiconformal extensions
    • Author(s): Chiang, Y.M.
    • Source: Annales Universitatis Mariae Curie-Sklodowska.Sectio A. Mathematica. , . 45, 1991, p. 21-27
    • Year: 1991

  Conference paper

1. Galoisian Approach to Complex Oscillation Theory
   • Author(s): Chiang, Yik Man; Yu, Guofu
   • Year: 2016


2. When Does a Formal Finite-difference Expansion Become Real?
   • Author(s): Feng, Shaoji; Chiang, Yik Man
   • Year: 2016


3. Galoisian Approach to Complex Oscillation of Hill's Eqauations
   • Author(s): Yu, Guofu; Chiang, Yik Man
   • Year: 2016


4. A Galoisian Approach to Complex Oscillation Theory
   • Author(s): Chiang, Yik Man; Yu, Guofu
   • Year: 2016


5. Complex Oscillation Theory and Semi-finite Gap Problems
   • Author(s): Luo, Xudan; Chiang, Yik Man
   • Year: 2016


6. Estimates on the growth of meromorphic solutions of linear differential equations with density conditions
   • Author(s): Chiang, Yik Man
   • Source: Reports and Studies in Forestry and Natural Sciences. , v. 14, p. 45-55
   • Year: 2014


7. Eigen-solutions of Biconfluent Heun equation with respect to a complex weight
   • Author(s): Chiang, Yik Man
   • Source: Colloquium on Jordan Theory and Analysis. , 8-12 April 2010
   • Year: 2010


8. A q-deformation of Nevanlinna Theory
   • Author(s): Chiang, Yik Man
   • Source: Conference on Value Distribution Theory and Complex Geometry. , 27-30 July 2009
   • Year: 2009


9. A q-deformation of classical Nevanlinna theory
   • Author(s): Chiang, Yik Man
   • Source: International Conference on Complex Analysis and Related Topics. , 20-23 August 2009, Beijing
   • Year: 2009


10. Malmquist-type theorems for second-order ODEs
    • Author(s): Chiang, Yik-Man
    • Source: International Conference on Nonlinear Waves: Theory and Applications, Beijing, China, organised by M. Ablowitz, D-Y. Hsieh and J. Yang. , 9-12 June 2008
    • Year: 2008


11. On The Nevanlinna Order Of Lommel And Struve Functions And Complex Differential Equations
    • Author(s): Chiang, Yik-Man
    • Source: The 9th International Conference on Special Functions, Orthogonal Polynomials and their Applications, Marseille, France, organized by G. Valent. , 2-6 July 2007 (30 minutes talk)
    • Year: 2007


12. On the Nevanlinna Order of Lommel, Struve Functions and Complex Differential Equations
    • Author(s): Chiang, Yik-Man
    • Source: 1st Joint Meeting of American and the Newzealand Mathematical Societies, Special session on Special Functions and Orthogonal Polynomials, Victoria Univ. of Wellington, organized by D. Dominici, O. Warnaar, S. Cooper. , 12-15 December 2007 (25 minutes invi
    • Year: 2007


13. Estimates of difference operators in the complex plane
    • Author(s): Chiang, Yik-Man
    • Source: The Painleve Equations and Monodromy Problems: Recent Developments, Newton Institute, Cambridge September 2006.
    • Year: 2006


14. Structural results of orthogonal polynomials that generalize Lommel's polynomials
    • Author(s): Chiang, Yik-Man
    • Source: ICM06 satelite meeting: 'Recent Trends in Constructive Approximation Theory', Univ. Carlos III de Madrid.
    • Year: 2006


15. Some Nevanlinna-type estimates related to discrete equations
    • Author(s): Chiang, Yik-Man; Feng, S.J.
    • Source: International Conference on Nonlinear Waves, Integrable Systems, and their Applications, in honor of Mark Ablowitz's sixtieth birthday, University of Colorado Spring, , organized by M. Kruskal, T. Fokas, S. Chakravarty and R. Cascaval. , 4--8th June 2005
    • Year: 2005


16. On the growth of entire solutions to some difference equations
    • Author(s): Chiang, Yik-Man; Feng, S.J.
    • Source: Computational Methods and Function Theory 2005, University of Joensuu, Finland, organized by St. Ruscheweyh, E. B. Saff, O. Martio and I. Laine.. , 13--17th June 2005,
    • Year: 2005


17. On The Location of Complex Zeros of Bessel Functions and Complex Oscillation Theory
    • Author(s): Chiang, Yik-Man; Ismail, Mourad E.M.
    • Source: American Mathematics Society, Joint Mathematics Meetings, Phoenix, AZ. Special Session in 'Value Distribution Theory in Classical and p-adic Function Theory', organized by A. Escassut, I. Laine and C. C. Yang.. , January 7-10
    • Year: 2004


18. On Value Distribution Theory, Complex Oscillation of Differential Equations and Special Functions
    • Author(s): Chiang, Yik-Man
    • Source: Summer School in Complex Difference Equations, August, University of Joensuu (Mekrijarvi Research Station).
    • Year: 2001


19. On Value Distribution Theory, Complex Oscillation of Differential Equations and Bessel polynomials
    • Author(s): Chiang, Yik-Man
    • Source: Summer School/Seminar in Applied Analysis, July, City University of Hong Kong.
    • Year: 2001


20. Efficient Software Multicast in Wormhole-Routed Unidirectional Multistage Networks
    • Author(s): Chiang, Chi-Ming; Ni, Lionel Ming-Shuan
    • Source: Proceedings of the Seventh IEEE Symposium on Parallel and Distributed Processing, Los Alamitos, CA : IEEE Computer Society Press, 1995, p. 106-113
    • Year: 1995

  Preprint

1. Two integrable differential-difference equations derived from NLS-type equation
   • Author(s): Xu, Zong-Wei; Yu, Guo-Fu; Chiang, Yik-Man
   • Source: arXiv, Mar 2015, Article number 1503.09073
   • Year: 2015


2. Nevanlinna theory of the Askey-Wilson divided difference operator
   • Author(s): Chiang, Yik-Man; Feng, Shaoji
   • Source: arXiv, Feb 2015, Article number 1502.02238
   • Year: 2015