Assistant Professor CHAN Song Heng

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 Publications 1.     A new identity for $(q;q)_10^\infty$ with an application to Ramanujan's partition congruence modulo 11, Quart. J. Math., 55 (2004), no. 1, 13--30. (Joint work with B. C. Berndt, Z.--G. Liu, and H. Yesilyurt.) 2.     Dissections of quotients of theta-functions, Bull. Austral. Math. Soc. 69 (2004), no. 1, 19--24. 3.     Domb's numbers and Ramanujan-Sato type series for 1/$\pi$, Adv. Math., 186 (2004), no. 2, 396--410. (Joint work with H. H. Chan and Z.--G. Liu.) 4.     An elementary proof of Jacobi's six squares theorem, Amer. Math. Monthly, 111 (2004), no. 9, 806--811. 5.     Ramanujan and cranks, in Theory and Applications of Special Functions. A Volume Dedicated to Mizan Rahman, M. E. H. Ismail and E. Koelink, eds., Kluwer, Dordrecht, 2005, 77--98. (Joint work with B. C. Berndt, H. H. Chan, and W.--C. Liaw.) 6.     Cranks and dissections in Ramanujan's lost notebook, J. Combin. Theory Ser. A, 109 (2005), no. 1, 91--120. (Joint work with B. C. Berndt, H. H. Chan, and W.--C. Liaw.) 7.     A short proof of Ramanujan's famous $_1\psi_1$ summation formula, J. Approx. Theory, 132 (2005), no. 1, 149--153. 8.     Generalized Lambert series identities, Proc. London Math. Soc., 91 (2005), no. 3, 598--622. 9.     The Periodicity of the Signs of the Coefficients of Certain Infinite Products, Pacific J. Math, 225 (2006), 12--32. (Joint work with H. Yesilyurt.) 10.  A reciprocity theorem for certain q-series found in Ramanujan's lost notebook, Special issue of the Ramanujan Journal in honor of R. Askey's 70th birthday, Ramanujan J., 13 (2007), no. 1-3, 27--37. (Joint work with B. C. Berndt, B. P. Yeap, and A. J. Yee.) 11.  Sixth order mock theta functions, Adv. Math., 216 (2007), no.2, 771--786. (Joint work with B. C. Berndt.) 12.  Congruences for Andrews-Paule's broken $k$-diamond partition function, Discrete Math., 308 (2008), no.23, 5735--5741. 13.  On Sears's general transformation formula for basic hypergeometric series, Ramanujan J., 20 (2009), 69--79. 14.  The Rogers-Ramanujan continued fraction and a new Eisenstein series identity, J. Number Theory, 129 (2009), no. 7, 1786--1797. (Joint work with H. H. Chan and Z.--G. Liu.) 15.  Cranks -- Really the Final Problem , Special issue of the Ramanujan Journal in honor of G.E. Andrews’s 70th birthday, Ramanujan J., published online: 01 October 2009. (Joint work with B. C. Berndt, H. H. Chan, and W.--C. Liaw.) 16.  On a new circular summation of theta functions, J. Number Theory, 130 (2010), no. 5, 1190--1196. (Joint work with Z.—G. Liu.) 17.  Analogs of the Stern sequence, Integers, 11 (2011), A26. 18.  Two congruences for Appell-Lerch sums, Int. J. Number Theory, 8 (2012), no.1, 111-123. (Joint work with R. Mao.) 19.  Congruences for Ramanujan’s $\phi$ function, Acta Arith., 153 (2012), no. 2, 161--189. 20.  Pairs of Partitions without repeated odd parts, J. Math. Anal. Appl., 394 (2012), 408--415. (Joint work with R. Mao.) 21.  The Odd Moments of Ranks and Cranks, J. Combin. Theory Ser. A, 120 (2013), 77--91. (Joint work with G. E. Andrews and B. Kim.) 22.  Rank-Crank type PDEs and generalized Lambert series identities, Special issue of the Ramanujan Journal in honor of Mourad Ismail and Dennis Stanton, 31 (2013), no.1—2, 163--189. (Joint work with A. Dixit and F.G. Garvan.) 23.  Inequalities for ranks of partitions and the first moment of ranks and cranks of partitions, Adv. Math., 258 (2014), 414--437. (Joint work with R. Mao.) 24.  The first positive rank and crank moments for overpartitions, Ann. Comb., to appear. (Joint work with G. E. Andrews, B. Kim, and R. Osburn.) 25.  The rank and crank of partitions modulo 3, Int. J. Number Theory, to appear. (Joint work with R. Mao.) 26.  On Recursions for coefficients of mock theta functions, submitted. http://arxiv.org/abs/1502.01429 (Joint work with R. Mao and R. Osburn.)

 Local Publication 1.     The q-binomial theorem, Mathematical Medley, Vol. 33 (2007), no.2. (Joint work with H. H. Chan and S. Cooper.) 2.     How to derive formulas for sums of consecutive powers, Mathematical Medley, Vol. 38 (20012), no.2. (Joint work with H. H. Chan.)

 Refereed Conference Proceedings 1.     A new proof of Winquist’s identity, Ramanujan Rediscovered: Proceedings of a Conference on Elliptic Functions, Partitions, and $q$-Series in memory of K. Venkatachaliengar: Bangalore, 1-5 June, 2009.

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