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., to appear. (Joint work with B. C. Berndt, H. H. Chan, and W.--C. Liaw.)

16.  On a new circular summation of theta functions, submitted. (Joint work with Z.—G. Liu.)

17.  Analogs of the Stern sequence, preprint.

 

Local Publication

1.     The q-binomial theorem, Mathematical Medley, Vol. 33 (2007), no.2. (Joint work with H. H. Chan and S. Cooper.)

 

Refereed Conference Proceedings

1.     A new proof of Winquist’s identity, submitted.

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