Publication List (not all articles are available)

New proofs of Ramanujan's partition identities for moduli 5 and 7. Journal of Number Theory, 53, (1995), 144-159.

Some values for the Rogers-Ramanujan continued fraction. Canadian Journal of Mathematics, 20, (1995), 1-18. (Joint paper with B. C. Berndt.)

Ramanujan's explicit values for the classical theta-function. Mathematika, 42, (1995), 278-294. (Joint paper with B. C. Berndt.)

On Ramanujan's cubic continued fraction. Acta Arithmetica, 73, no. 4, (1995), 343--355.

Ramanujan's class invariants and cubic continued fraction. Acta Arithmetica, 73, no. 1, (1995), 67--85. (Joint paper with B. C. Berndt, and L.-C. Zhang.)

On the equivalence of Ramanujan's partition identities and a connection with the Rogers-Ramanujan continued fraction. Journal of Mathematical Analysis and Applications, 198, (1996), 111--120.

Explicit evaluations of the Rogers-Ramanujan continued fraction. Journal fur die reine und angewandte Mathematik (Crelle) 480, (1996), 141--159. (Joint paper with B. C. Berndt, and L.-C. Zhang)

On Ramanujan-Gordon Quadratic Continued Fraction. The Ramanujan Journal. 1, (1997), 75–90. (Joint paper with S.-S. Huang)

Ramanujan’s class invariants with applications to the values of q-continued fractions and theta functions. Fields Institute Communications, 14, (1997), 37–53. (Joint paper with B.C. Berndt, and L.-C. Zhang)

Ramanujan’s class invariants, Kronecker’s Limit Formula, and Modular Equations. Transactions of the AMS. 349, (1997), no. 6, 2125–2173. (Joint paper with B. C. Berndt, and L.-C. Zhang)

Ramanujan’s singular moduli. The Ramanujan Journal. 1, (1997), 53–74 (Joint paper with B. C. Berndt, and L.-C. Zhang)

Ramanujan’s Remarkable Product of Theta-functions. Proceedings of the Edinburgh Mathematical Society. 40 (1997), Part 3, 583–612. (Joint paper with B. C. Berndt, and L.-C. Zhang)

Ramanujan's association with radicals in India. Amer. Math. Monthly. 104, (1997), 913--919 (Joint work with B. C. Berndt and L.-C. Zhang)

Ramanujan's modular equations and the Atkin-Lehner Involutions. Israel Journal of Mathematics. 103, (1998), 1--16 (Joint paper with M.-L. Lang)

On Ramanujan's transformation formula for $_2F_1(1/3,2/3;1;z).$ Mathematical Proceedings of the Cambridge Philosophical Society. 124, (1998), 193-204.

Ramanujan's class invariants and Watson's empirical process. Journal of London Mathematical Society, series 2, 57, (1998), 545-561.

Notes on Ramanujan's Singular Moduli. The Proceedings of the Fifth Conference of the Canadian Number Theory Association, edited by R. Gupta and K.S. Williams, (1998), 7-16. (Joint paper with B.C. Berndt).

Radicals and units in Ramanujan's work. Acta Arithmetica. 87, no. 2 (1998), 145-158. (Joint work with B.C. Berndt and L.C. Zhang)

Eisenstein Series and $\sum_{m,n=-\infty}^\infty q^{m^2+mn+2n^2}$. Proceedings of the American Mathematical Society. 127, no. 6, (1999), 1735-1744. (Joint work with Y. L. Ong)

The Rogers-Ramanujan continued fraction. Journal of Computational and applied mathematics. 105, (1999), 9-24. (Joint work with B.C. Berndt, S.S. Huang, S.Y. Kang, J. Sohn and S.H. Son )

On explicit evaluations of the Rogers-Ramanujan continued fraction. Contemporary Mathematics (AMS), 236, (1999), 127-136. (Joint work with V. Tan)

Ramanujan and the Modular $j$--invariant. Canadian Mathematical Bulletin, 42, no. 4, (1999), 427-440. (Joint work with B. C. Berndt)

Cubic modular equations and new Ramanujan-type series for $1/\pi$. Pacific J. Math. 192, (2000), 219-238. (Joint work with W.C. Liaw)

On Russell-type modular equations. The Canadian Journal of Mathematics, 52 ,(2000), 31-46. (Joint work with W.C. Liaw)

Incomplete elliptic integrals in Ramanujan's Lost Notebook. Contemporary Mathematics (AMS), 254, (2000), 79-126: Proceedings of a conference in honour of Professor Richard Askey. (Joint work with B.C. Berndt and S.S. Huang)

Eisenstein Series in Ramanujan's Lost Notebook. The Ramanujan Journal, 4, no. 1 (2000), 81-114. (Joint work with B.C. Berndt, J.B. Sohn and S.H. Son)

A page on Eisenstein Series and approximations to $\pi$ from Ramanujan's Lost Notebook. Illinois J. Math., 45, no.1 (2001), 75-90. (Joint work with B.C. Berndt)

On Ramanujan's quartic theory of elliptic functions. J. Number Theory, vol. 88, no. 1, (2001), 129-156. (Joint work with B.C. Berndt and W.C. Liaw)

Ramanujan's class invariant $\lambda_n$ and a new class of series for $1/\pi$. J. London Math. Soc., 64, no.1, (2001), 93-106. (Joint work with W.C. Liaw and V. Tan)

A certain quotient of eta-functions found in the Lost Notebook. Pacific J. Math., vol. 202, no. 2, (2002), 267-304. (Joint work with B.C. Berndt, S.Y. Kang and L.C. Zhang)

Ramanujan's elliptic functions to alternative bases and approximations to $\pi$. Number Theory for the Millennium I (Proceedings of the Millennial Number Theory Conference, Champaign-Urbana, Illinois, May 2000), Bruce Berndt, et.al., editors, A.K. Peters Ltd, 2002.

New Ramanujan-Kolberg type identities. Mathematical Research Letters, 9, (2002), 801-811. (Joint work with H. Hahn, R.P. Lewis, S.L. Tan)

Two quadratic iterations to $\pi$ associated with elliptic functions to alternative bases. Trans. Amer. Math. Soc. 355, (2003), 1505-1520. (Joint work with K.S. Chua and P. Sole)

Cubic Singular Moduli, Ramanujan's class invariant $\lambda_n$ and the explicit Shimura Reciprocity Law. Pacific J. Math., 208, (2003) , no. 1, 23-37.(Joint work with A. Gee and V. Tan).

A Quasi-theta Product in Ramanujan's Lost Notebook. Math. Proc. Camb. Phil. Soc., 135, (2003), p. 11-18. (Joint work with B.C.Berndt and Alexandru Zaharescu)

Analogues of Jacobi's inversion formula for the incomplete elliptic integral of the first kind. Advances in Mathematics, 174, (2003), 69-88. (Joint work with Z.G. Liu)

7-modular lattices and a septic base Jacobi identity. J. Number Theory, 99, (2003), 361-372. (Joint work with K.S.Chua and P.Sole)

Representations of integers as sums of 32 squares. The Ramanujan Journal, 7, (2003), 79-90.(Joint work with K.S.Chua)

Partition identities and Congruences associated with the Fourier coefficients of the Euler products. Journal of Computational and Applied Math., 160 (2003) 69-75. (Joint work with R.P. Lewis)

Domb's numbers and Ramanujan-Sato type series for $1/\pi$. Advances in Math., 186 (2004) 396-410 (with S.H. Chan and Z.G. Liu).

Cranks and dissections in Ramanujan's Lost Notebook. J. Combin. Theory Ser. A 109 (2005), no. 1, 91--120, (with B.C. Berndt, S.H. Chan and W.C. Liaw).

Ramanujan and cranks. in Theory and applications of special functions, 77--98, Dev. Math., 13, Springer, New York, 2005, (with B.C. Berndt, S.H. Chan and W.C. Liaw).

Recent progress in the study of the representations of integers as sums of squares. Bull. of the London Math. Soc. 37 (2005), 818-826. (with Christian Krattenthaler)

Elliptic functions and the Quintuple, Hirschhorn and Winquist product identities. International Journal of Number Theory 1 (2005), 33-43. (with Zhi-Guo Liu and Say Tiong Ng).

Circular summation of theta functions in Ramanujan's lost notebook. Journal of Mathematical Analysis and applications 316 (2006), 628-641. (with Zhi-Guo Liu and Say Tiong Ng).

The $26^{\text{th}}$ power of Dedekind's $\eta$ function Advances of Mathematics 207 (2006), 532-543. (with S. Cooper and Pee Choon Toh).

Elliptic functions to the quintic base. Pacific Journal of Mathematics 226 (2006), no.1, 53-64. (with Zhi-Guo Liu).

Ramanujan's Eisenstein series and powers of Dedekind's eta-function Journal of the London Mathematical Society, (2) 75 (2007), no. 1, 225-242. (with S. Cooper and P.C. Toh)

Ramanujan's cubic continued fraction revisited, Acta Arithmetica 126 (2007), no. 4, 305-313. (with Kok Ping Loo)

Triple product identity, quintuple product identity and Ramanujan's differential equations for the classical Eisenstein series Proc. of the Amer. Math. Soc., 135 (2007), no. 7, 1987-1992.

The Rogers-Ramanujan continued fraction and a quintic iteration for $1/\pi$ Proc. of the Amer. Math. Soc., 135 (2007), no. 11, 3417-3424. (with Shaun Cooper and W.C. Liaw)

Powers of theta functions. Pacific J. Math. 235 (2008), no. 1, 1--14. (with Shaun Cooper)

Eisenstein series and theta functions to the septic base. J. Number Theory 128 (2008), no. 3, 680--699. (with Shaun Cooper)

A squares as a sum of odd number of odd squares. Acta Arithmetica 132, no. 4 (2008), 359-371. (with Shaun Cooper and Wen-Chin Liaw)

On $\eta^3(a\tau)\eta^3(b\tau)$ with $a+b=8$. J. Aust. Math. Soc., 84 (2008), 301-313. (with Shaun Cooper and Wen-Chin Liaw)

The Almkvist-Zudilin numbers and new series for $1/\pi$. Mathematical Research Letters, 16 (2009), no. 3, 405-420. (with H.A. Verrill)

The Rogers-Ramanujan continued fraction and a new Eisenstein series identity. J. Number Theory, 129 (2009), 1786-1797. (with S.H. Chan and Z.G. Liu)

Ramanujan's series for $1/\pi$: A survey. Math. Student 2007, Special Centenary Volume, 1--24 (2008) AND Amer. Math. Monthly 116 (2009), no. 7, 567--587. (with N.D. Baruah and B.C. Berndt)

Congruences satisfied by Apery-like numbers. International J. of Number Theory, Volume: 6, Issue: 1(2010) pp. 89-97. (with S.Cooper and F.Sica)

New representations for Apery-like sequences Mathematika, 56 (2010) , pp 107-117. (with W. Zudilin)

Supercongruences satisfied by coefficients of $_2F_1$ hypergeometric series Annales des sciences mathematiques du Qu?bec (special issue dedicated to P. Ribenboim), vol. 34, no.1, (2010), 25--36. (with A. Kontogeorgis, C. Krattenthaler and R. Osburn)

A supercongruence motivated by the Legendre family of elliptic curves, Mathematical Notes, vol 88, no. 4 (2010), 599--602. Also appeared in Russian in Matematicheskie Zemetki 2010, vol 88, no. 4, 620-624. (with Ling Long, W. Zudilin)

New Ramanujan type partition identities. Journal of Number Theory, vol. 130 (2010), 1898-1913. (with Pee Choon Toh)

Cranks-really, the final problem. The Ramanujan Journal, vol. 23 (2010), no. 1--3, 3-15. (with B.C. Berndt, S.H. Chan, W.C. Liaw)

The Cubic Analogue of the Jacobsthal sum. Amer. Math. Monthly, vol 118 (2011), no. 4, 316-326. (with Ling Long, YiFan Yang)

New analogues of Clausen's identities arising from the theory of modular forms. Advances in Mathematics, vol. 228 (2011), issue 2, 1294-1314. (with Y. Tanigawa, W. Zudilin and YiFan Yang)

Rational analogues of Ramanujan's series for $1/\pi$. Math. Proc. Camb. Phil. Soc., vol. 153 (2012), issue 2, 361-383. (with S. Cooper)

Two Dirichlet series found on page 196 of Ramanujan's Lost Notebook Math. Proc. Camb. Phil. Soc., Math. Proc. Camb. Phil. Soc., vol. 153 (2012), issue 2, 341-360. (with B.C. Berndt and Y. Tanigawa)

What is your birthday elliptic curves? Finite fields and its applications, vol. 18 (2012), 1232-1241. (with E. Konstantinou, A. Kontogeorgis, C. H. Tan)

Complex series for $1/\pi$ Ramanujan J. vol. 29, Issue 1 (2012), 135-144. (with J. Wan and W. Zudilin)

The Bailey-Brafman identity and its analogues. Journal of Mathematical Analysis and Applications, vol. 399 (2013), 12-16.

Legendre polynomials and Ramanujan-type series for $1/\pi$. Israel J. Math. 194 (2013), no. 1, 183-207. (with J. Wan and W. Zudilin)

A generalization of a Brafman-Bailey type identity. Proc. Amer. Math. Soc., vol. 143, no.1 (2015), 185-195. (with Y. Tanigawa)

Analogues of the Brent-Salamin algorithm for evaluating $\pi$. The Ramanujan Journal, vol. 38, no. 1 (2015), 75-100.

Theta series associated with certain positive definite binary quadratic forms. Acta Arithmetica, vol. 169, no. 4, (2015), 331-356. (with Pee Choon Toh)

An alternative transformation formula for the Dedekind $\eta$-function via the Chinese Remainder Theorem. International Journal of Number Theory, vol. 12, no. 2, (2016), 513-526. (with Teoh Guan Chua)

Congruences modulo 5 and 7 for 4-colored generalized Frobenius partitions. Journal of the Australian Mathematical Society, 1-20. Online publication date: 21-Dec-2016. (with LiuQuan Wang and YiFan Yang).

Congruences associated with the modular $j$-invariant, Integers 17 (2017) A25. (with Si Ying Lee)

On certain identities of Hecke type, New Zealand Journal of Mathematics, vol. 48, (2018), Pages 1-10. (with Z.G. Liu)

Wronskians of theta functions and series for $1/\pi$, Advances in Mathematics, 338 (2018), 266–304. (with A. Berkovich and M. Schlosser)

Modular forms and $k$-colored generalized Frobenius partitions, Trans. Amer. Math. Soc. 371 (2019), no. 3, 2159–2205. (with LiuQuan Wang and YiFan Yang)

Fractional powers of the generating function for the partition function, Acta Arithmetica, Acta Arith. 187 (2019), no. 1, 59–80. (with LiuQuan Wang)

On a symmetric identity of Ramanujan involving the sum of two squares function, Journal of Mathematical Analysis and Applications, 473 (2019), no. 2, 1234–1243. (with Pee Choon Toh)

Fine's functions and partial theta functions, Proc. Amer. Math. Soc. 149 (2021), no. 6, 2561–2572. (with Song Heng Chan, Kuo-Jye Chen and Sen Shan Huang)

Multiplicative functions arising from the study of mutually unbiased bases, New Zealand J. Math. 51 (2021), 65–78. (with Berthold-Georg Englert)

Borweins' cubic theta functions revisited, Ramanujan J. 57 (2022), no. 1, 55–70. (with LiuQuan Wang)

An amazing identity of Gauss and Jenkins' lemma, Bulletin of the Australian Math. Soc. 108, (2023), 86-98. (with Song Heng Chan)

On theorems of Fermat, Wilson, and Gegenbauer, appeared online on 8 September 2023, Canadian Math. Bulletin. (with Song Heng Chan, Teoh Guan Chua and Cheng Yeaw Ku)

The Fundamental Theorem of Arithmetic and $q$-series, Mathematics Magazine, (2024), DOI:10.1080/0025570X.2024.2312094. (with Kuo-Jye Chen and Warren P. Johnson)

Elementary derivations of the Rogers-Fine identity and other q-series identities, Discrete Mathematics, (2025). (with Song Heng Chan and ZhiGuo Liu)

An analogue of an identity of Jacobi, Bull. Aust. Math. Soc. (2025). (with Song Heng Chan and Patrick Sole)

Finite versions of the Andrews-Gordon identity and Bressoud's identity Journal of Combinatorial Theory, Series A (2025). (with Song Heng Chan)

Ramanujan's theory of elliptic functions to the cubic base Results in Mathematics (2025). (with Zhi-Guo Liu)

The quadratic reciprocity law and the Gauss-Schering lemma Contemp. Math. , 818 American Mathematical Society, [Providence], RI, 2025, 129–135. (with Chua, Teoh Guan)