Publications

Publications

K. M. Cheng, Y. M. Chiang and Avery Ching, "D-module approach to special functions and generating functions", Comptes Rendus Math\'{e}matiques de l'Acad\'{e}mie des Sciences. La Soci\'{e}t\'{e} Royale du Canada., 45, (2023), 1-12
K. M. Cheng, Y. M. Chiang and Avery Ching, "D-module approach to Liouville's theorems for differences operators", New Zealand Journal of Mathematics, 53, (2022), 63-79 (arXiv: 2109.06487)
Y. M. Chiang, Avery Ching and Chiu-Yin Tsang, "Resolving singularities of Heun connections and P_VI" arXiv:2009.02871 (published online 27th April 2021) Ann Henri Poincar\'e, 22 (2021), 3051-3094
K. H. Cheng and Y. M. Chiang, Wiman-Valiron theory of a polynomial series based on Askey-Wilson divided difference operator. arXiv:2001.02120 (Constructive Approximation 2021: https://link.springer.com/article/10.1007/s00365-021-09528-3)
Y. M. Chiang and Guofu Yu, "Galoisian approach to complex oscillation theory of Hill equations" (https://arxiv.org/abs/1610.09757) Mathematica Scandinavica, 124, no. 1 (2019), 102-131.
Y. M. Chiang and S. J. Feng "Nevanlinna theory based on Askey-Wilson divided difference operator", (https://arxiv.org/abs/1502.02238), (proof), Advances in Mathematics, 329, (2018), 217-272.
Y. M. Chiang, A. Ching and C. Y. Tsang , "Symmetries of the Darboux equation" (http://arxiv.org/abs/1509.03995). Kumamoto Journal of Mathematics, 31, (2018), 15-48.
Y. M. Chiang and Xudan Luo, "Difference Nevanlinna theories with vanishing and infinite periods"(http://arxiv.org/abs/1510.02576 : there are a number of changes, updated will be done later, so please refer to the publihsed version in MMJ), Michigan Mathematical Journal, Vol. 66, no. 3 (2017), 451-480.
K.-H. Cheng and Y. M. Chiang, "Nevanlinna theory based on Wilson divided difference operator", http://arxiv.org/abs/1606.05575, Annales Academiae Scientiarum Fennicae. Series A I., Mathematica 42 (2017) no. 2, 175-209
Y. M. Chiang and S. J. Feng, "On the growth of logarithmic difference of meromorphic functions and a Wiman-Valiron estimate", http://arxiv.org/abs/1309.4211 Constructive Approximations, 44 no. 3 (2016) 313-326 (http://link.springer.com/article/10.1007/s00365-016-9324-8)
Y. M. Chiang, "Estimates on the growth of meromorphic solutions of linear differential equations with density conditions", Reports and Studies in Forestry and Natural Sciences No 14, 45-55, 2014, Univ. Eastern Finland http://arxiv.org/abs/1311.1874
Y. M. Chiang and K. W. Yu, "On complex oscillation, function-theoretic quantization of non-homogeneous periodic ODEs and special functions", Proceedings of Royal Society of Edinburgh, 142A (2012) 449-477 (http://arxiv.org/abs/1002.3853)

Y. M. Chiang and K. W. Yu, "Subnormal solutions of non-homogeneous periodic ODEs, special functions and special polynomials" Journal für die reine und angewandte Mathematik (Crelle's Journal) 651(2011) 127-164 (arXiv: 0906.4659).
Y. M. Chiang and S. J. Feng, "On the growth of logarithmic differences, difference quotients and logarithmic derivatives of meromorphic functions", Transaction of American Mathematical Society 361, no. 7 (2009) 3767-3791 (arXiv: math/0610480)
Y. M. Chiang and S. J. Feng, "On the growth of $f(z+\eta)$ and difference equations in the complex plane", The Ramanujan Journal 16 (2008) 105-129 (arXiv: math/0609324v3)
Y. M. Chiang and S. J. Feng, "Difference independence of Riemann Zeta function", Acta Arithmetica, 125 (4) 2006, 317-329. (arXiv: math/0610479)
Y. M. Chiang and S. N. M. Ruijsenaars, "On the Nevanlinna order of meromorphic solutions to linear analytic
difference equations", Studies in Applied Mathematics, 116, (2006) 257--287.
Y. M. Chiang and M. E. H. Ismail, "On value distribution theory of second order periodic ODES, special functions and
orthogonal polynomials", Canadian Journal of Mathematics, 58, (2006) 726--767. (Corrigendum Canadian Journal of Mathematics, 62, (2010) p, 261)
Y. M. Chiang and W. K. Hayman, "Estimates on the growth of entire and meromorphic solutions of linear differential equations",
Commentarii Mathematici Helvetici, 79 (2004), 451--470.
Y. M. Chiang and R. G. Halburd, "On the meromorphic solutions to an equation of Hayman", Journal of Mathematical Analysis and Applications, 281 (2003), 663--677.
Y. M. Chiang and M. E. H. Ismail, ``Complex oscillation theory and special functions", Mathematical Reports of
the Academy of Science of Canada, 24 No. 3, 2002. (research announcement).
Y. M. Chiang and S. Gao, "On a problem in oscillation theory of periodic second order linear differential equations and
some related perturbation results", Annales Academiae Scientiarum Fennicae. Series A I. Mathematica, 27 (2002), 273-290.
Y. M. Chiang, "On the zero-free solutions of linear periodic differential equations in the complex plane", Results in Mathematics, 38 (2000), 213-225.
Y. M. Chiang and I. Laine, "Some oscillation results for linear differential equations in the complex plane", Japanese J. of
Math., 24 (2), (1998), 367-402.
Y. M. Chiang and S. Wang, "Oscillation results of certain higher order linear differential equations with periodic coefficients in the complex plane", Journal of Mathematical Analysis and Applications., 215 (1997), 560-576.
Y. M. Chiang, I. Laine and S. Wang, "On complex oscillation of a third order linear periodic differential equation in the complex
plane", Complex Variables. Theory and Application, 34 (1997), 25--34.
Y. M. Chiang, "On the complex oscillation of $y''+(e^z-K)y=0$ and a result of Bank, Laine and Langley", Proc. Computational Methods and Function Theory, Series in Approximations and Decompositions--Vol. 5, World Scientific 1995, 125--134 (refereed).
Y. M. Chiang, I. Laine and S. Wang, "Oscillation results for some linear differential equations", Mathematica Scandinavica, 77 (1995), 209--224.
Y. M. Chiang, "Oscillation results on y''+Ay=0 in the complex domain with transcendental entire coefficients which have extremal deficiencies", Proceedings of the Edinburge Mathematical Societry, 35 (1995), 13--34.
Y. M. Chiang, "Some properties of analytic functions with small schwarzian", Complex Variables: Theory and Applications, 25 (1994), 107--118.
Y. M. Chiang, "Some remarks on Lehto's domain constant", Annales Academiae Scientiarum Fennicae. Series A I.
Mathematica., 17 (1992), 285--293.
Y. M. Chiang, "On a subclass of strongly gamma--starlike functions and quasiconformal extensions", Annales Universitatis Mariae Curie--Sklodowska. Sectio A. Mathematica ., 45 (1991), 21--27.

Papers availbile online:

Y. M. Chiang, A. Ching and C. Y. Tsang, ``Solutions of Darboux equations, its degeneration and Painlev\'e VI equations", arXiv: 1901.03102
Y. M. Chiang, Chun-Kong Law and Guofu Yu, ``Invariant subspaces of biconfluent Heun operators and special solutions of Painlev\'e IV", arXiv: 1905.10046
Y. M. Chiang, Avery Ching and Chiu Yin Tsang, ``Series solutions of linear ODEs by Newton-Raphson method on quotient D-modules", arXiv: 2111.05103
Y. M. Chiang, Avery Ching and Xiaoli Lin, ``Holonomic Bessel modules and generating functions", arXiv: 2303.15496

Papers under construction:

Y. M. Chiang and K.W. Yu "On asymptotic of zeros of Lommel functions"
Y. M. Chiang, R. H. Halburd and E. Lingham "Malmquist-type theorems for the Painleve equations"
Y. M. Chiang and Xudan Luo, "On complex oscillation and semi-infinite gaps of Whittaker-Hill equation"
Y. M. Chiang and M. E. H. Ismail, "Lommel polynomials for confluent hypergeometric equations"

Current PhD research students:

Lin, Xiaoli

Previous PhD students:

Dr. Kit-Wing Yu (August, 2010),
Dr. Xudan Luo (July 2016)),
Dr. Kam Hang Cheng (Henry) (January 2017)

Previous MPhil students:

Meng, Bin (2021)
Cheung, Tsz Yung (2019)
Kwan, Tony (1999, later PhD, currently at CGGVeritas, US Seismic Imager)
Lo, Man Ho (1997)

Current Postdoc:

Dr. Kam Hang Cheng (Henry)

Previous Postdoc:

Dr. Guofu Yu (now at Shanghai JiaoTong University)
Dr. Chiu Yin Tsang (The Hong Kong University)

CV

Recemt Talks:

裘錦秋中學（元朗）(School talk given in Ju Ching Chu Secondary School (Yuen Long) 3rd March 2017

Google citation: http://scholar.google.com/citations?hl=en&user=cImFOsAAAAAJ
MathSciNet (AMS): http://www.ams.org/mathscinet/mrcit/individual.html?mrauthid=350575
arXiv.org: http://arxiv.org/find/math/1/au:+Chiang_Y/0/1/0/all/0/1