Associate Professor Shaun Cooper

Associate Professor Shaun Cooper staff profile picture

Associate Professor

Institute of Natural and Mathematical Sciences

Contact details
Telephone: +64 (09) 414 0800  ext. 43604
Email: 

Research Outputs

Journal

Cooper, S., Ge, J., & Ye, D. (2014). Hypergeometric transformation formulas of degrees 3, 7, 11 and 23. Journal of Mathematical Analysis and Applications.
[Journal article]Authored by: Cooper, S.
COOPER, S., & YE, D. (2014). EISENSTEIN SERIES TO THE TREDECIC BASE. Bulletin of the Australian Mathematical Society.
[Journal article]Authored by: Cooper, S.
Cooper, S., & Ye, D. (2014). The Rogers-Ramanujan continued fraction and its level 13 analogue. Journal of Approximation Theory.
[Journal article]Authored by: Cooper, S.
Cooper, S., & Ye, D. (2014). Evaluation of the convolution sums Σ<inf>l+20m=n</inf> σ(l)σ(m), Σ<inf>4l+5m=n</inf> σ(l)σ(m) and Σ<inf>2l+5m=n</inf> σ(l)σ(m). International Journal of Number Theory. 10(6), 1385-1394
[Journal article]Authored by: Cooper, S.
Cooper, S., & Ye, D. (2014). Evaluation of the convolution sums ∑l+20m=n σ(l)σ(m), ∑4l+5m=n σ(l)σ(m) and ∑2l+5m=n σ(l)σ(m). International Journal of Number Theory. (2)
[Journal article]Authored by: Cooper, S.
Cooper, S., & Ye, D. (2014). Explicit evaluations of a level 13 analogue of the Rogers-Ramanujan continued fraction. Journal of Number Theory. 139, 91-111
[Journal article]Authored by: Cooper, S.
Cooper, S., Lam, HY., & Ye, D. (2013). Representations of squares by certain quinary quadratic forms. Acta Arithmetica. 157(2), 147-168
[Journal article]Authored by: Cooper, S.
Cooper, S., & Lam, HY. (2013). On the Diophantine equation n <sup>2</sup>=x <sup>2</sup>+by <sup>2</sup>+cz <sup>2</sup>. Journal of Number Theory. 133(2), 719-737
[Journal article]Authored by: Cooper, S., Lam, H.
Cooper, S. (2012). Level 10 analogues of Ramanujan's series for 1/pi. JOURNAL OF THE RAMANUJAN MATHEMATICAL SOCIETY. 27(1), 59-76
[Journal article]Authored by: Cooper, S.
Cooper, S. (2012). Sporadic sequences, modular forms and new series for 1/π. Ramanujan Journal. 29(1-3), 163-183
[Journal article]Authored by: Cooper, S.
Chan, HH., & Cooper, S. (2012). Rational analogues of Ramanujan's series for 1/Ï. Mathematical Proceedings of the Cambridge Philosophical Society. 153(2), 361-383
[Journal article]Authored by: Cooper, S.
Cooper, S. (2012). Sporadic sequences, modular forms and new series for 1/π. Ramanujan Journal. , 1-21
[Journal article]Authored by: Cooper, S.
Cooper, S., & Hirschhorn, MD. (2011). Factorizations that involve Ramanujan's function k(q) = r(q)r2(q2). Acta Mathematica Sinica, English Series. 27(12), 2301-2308
[Journal article]Authored by: Cooper, S.
Cooper, S., & Lam, HY. (2011). Eisenstein series and elliptic functions on Γ0(10). Advances in Applied Mathematics. 46(1-4), 192-208
[Journal article]Authored by: Cooper, S., Lam, H.
Chan, HC., & Cooper, S. (2010). Congruences modulo powers of 2 for a certain partition function. Ramanujan Journal. 22(1), 101-117
[Journal article]Authored by: Cooper, S.
Cooper, S. (2010). Series and iterations for 1/π. Acta Arithmetica. 141(1), 33-58
[Journal article]Authored by: Cooper, S.
Chan, HH., Cooper, S., & Sica, F. (2010). Congruences satisfied by Apéry-like numbers. International Journal of Number Theory. 6(1), 89-97
[Journal article]Authored by: Cooper, S.
Cooper, S., & Toh, PC. (2009). Quintic and septic Eisenstein series. Ramanujan Journal. 19(2), 163-181
[Journal article]Authored by: Cooper, S.
Cooper, S. (2009). On Ramanujan's function k(q) = r(q)r<sup>2</sup>(q<sup>2</sup>). Ramanujan Journal. 20(3), 311-328
[Journal article]Authored by: Cooper, S.
Cooper, S. (2009). Inversion formulas for elliptic functions. Proceedings of the London Mathematical Society. 99(2), 461-483
[Journal article]Authored by: Cooper, S.
Cooper, S. (2009). Construction of eisenstein series for Γ0(p). International Journal of Number Theory. 5(5), 765-778
[Journal article]Authored by: Cooper, S.
Cooper, S. (2009). On the number of representations of integers by certain quadratic forms, II. Journal of Combinatorics and Number Theory. 1(2), 153-182
[Journal article]Authored by: Cooper, S.
Cooper, S., & Lam, HY. (2009). Sixteen Eisenstein series. Ramanujan Journal. 18(1), 35-59
[Journal article]Authored by: Cooper, S., Lam, H.
Chan, HH., Cooper, S., & Liaw, WC. (2008). ON η3(aτ)η3(bτ) with a+b=8. Journal of the Australian Mathematical Society. 84(3), 301-313
[Journal article]Authored by: Cooper, S.
Chan, HH., & Cooper, S. (2008). Powers of theta functions. Pacific Journal of Mathematics. 235(1), 1-14
[Journal article]Authored by: Cooper, S.
Cooper, S. (2008). The cubic Chan-Chua conjecture. Experimental Mathematics. 17(4), 439-442
[Journal article]Authored by: Cooper, S.
Cooper, S. (2011). On the number of representations of integers by certain quadratic forms, II. , 157-188
[Journal article]Authored by: Cooper, S.
Cooper, S., & Toh, PC. (2008). Determinant identities for theta functions. Journal of Mathematical Analysis and Applications. 347(1), 1-7
[Journal article]Authored by: Cooper, S.
Baruah, ND., Cooper, S., & Hirschhorn, M. (2008). Sums of squares and sums of triangular numbers induced by partitions of 8. International Journal of Number Theory. 4(4), 525-538
[Journal article]Authored by: Cooper, S.
Chan, HH., & Cooper, S. (2008). Eisenstein series and theta functions to the septic base. Journal of Number Theory. 128(3), 680-699
[Journal article]Authored by: Cooper, S.
Chan, HH., Cooper, S., & Liaw, WC. (2008). An odd square as a sum of an odd number of odd squares. Acta Arithmetica. 132(4), 359-371
[Journal article]Authored by: Cooper, S.
Chan, HH., Cooper, S., & Toh, PC. (2007). Ramanujan's eisenstein series and powers of Dedekind's eta-function. Journal of the London Mathematical Society. 75(1), 225-242
[Journal article]Authored by: Cooper, S.
Cooper, S., & Hirschhorn, M. (2007). On the number of primitive representations of integers as sums of squares. Ramanujan Journal. 13(1-3), 7-25
[Journal article]Authored by: Cooper, S.
Chan, HH., Cooper, S., & Liaw, WC. (2007). The Rogers-Ramanujan continued fraction and a quintic iteration for 1/π. Proceedings of the American Mathematical Society. 135(11), 3417-3424
[Journal article]Authored by: Cooper, S.
Cooper, S., Gun, S., & Ramakrishnan, B. (2006). On the lacunarity of two-eta-products. Georgian Mathematical Journal. 13(4), 659-673
[Journal article]Authored by: Cooper, S.
Cooper, S., & Hirschhorn, M. (2006). Sums of squares and sums of triangular numbers. Georgian Mathematical Journal. 13(4), 675-686
[Journal article]Authored by: Cooper, S.
Cooper, S. (2006). The quintuple product identity. INTERNATIONAL JOURNAL OF NUMBER THEORY. 2(1), 115-161
[Journal article]Authored by: Cooper, S.
Cooper, S. (2006). Cubic elliptic functions. Ramanujan Journal. 11(3), 355-397
[Journal article]Authored by: Cooper, S.
Chan, HH., Cooper, S., & Toh, PC. (2006). The 26th power of Dedekind's η-function. Advances in Mathematics. 207(2), 532-543
[Journal article]Authored by: Cooper, S.
Adiga, C., Cooper, S., & Han, JH. (2005). A GENERAL RELATION BETWEEN SUMS OF SQUARES AND SUMS OF TRIANGULAR NUMBERS. INTERNATIONAL JOURNAL OF NUMBER THEORY. 1(2), 175-182
[Journal article]Authored by: Cooper, S.
Cooper, S., Gun, S., Hirschhorn, M., & Ramakrishnan, B. (2005). Relations among Fourier coefficients of certain eta products. Integers: Electronic Journal of Combinatorial Number Theory. 5(1)
[Journal article]Authored by: Cooper, S.
Cooper, S., Hirschhorn, M., & Sellers, JA. (2005). Partitions into four squares. Proceedings of the Jangjeon Mathematical Society. 8(1), 73-94
[Journal article]Authored by: Cooper, S.
Cooper, S. (2005). Cubic theta functions in three variables. Proceedings of the Jangjeon Mathematical Society. 8(1), 19-24
[Journal article]Authored by: Cooper, S.
Cooper, S. (2005). A simple proof of an expansion of an eta-quotient as a Lambert series. Bulletin of the Australian Mathematical Society. 71(3), 353-358
[Journal article]Authored by: Cooper, S.
Cooper, S., & Hirschhorn, M. (2004). A combinatorial proof of a result from number theory. Integers: Electronic Journal of Combinatorial Number Theory. 4
[Journal article]Authored by: Cooper, S.
Adiga, C., Cooper, S., & H Han, J. (2004). General relations between sums of squares and sums of triangular numbers. Research Letters in the Information and Mathematical Sciences. 6, 157-161
[Journal article]Authored by: Cooper, S.
Cooper, S., & Hirschhorn, MD. (2004). Results of Hurwitz type for three squares. Discrete Mathematics. 274(1-3), 9-24
[Journal article]Authored by: Cooper, S.
Cooper, S., & Hirschborn, M. (2004). A combinatorial proof of a result from number theory. Integers. 4, A09
[Journal article]Authored by: Cooper, S.
Cooper, S. (2003). Cubic elliptic functions. Research Letters in the Information and Mathematical Sciences. 5, 23-59
[Journal article]Authored by: Cooper, S.
Cooper, S. (2003). Cubic theta functions. Journal of Computational and Applied Mathematics. 160(1-2), 77-94
[Journal article]Authored by: Cooper, S.
Cooper, S. (2003). On the number of representations of certain integers as sums of 11 or 13 squares. Journal of Number Theory. 103(2), 135-162
[Journal article]Authored by: Cooper, S.
Cooper, S. (2002). A q-analogue of Kummer's 20 relations. Journal of Mathematical Analysis and Applications. 272(1), 43-54
[Journal article]Authored by: Cooper, S.
Cooper, S. (2002). Sums of five, seven and nine squares. Ramanujan Journal. 6(4), 469-490
[Journal article]Authored by: Cooper, S.
Barrucand, P., Cooper, S., & Hirschhorn, MD. (2002). Results of Hurwitz type for five or more squares. Ramanujan Journal. 6(3), 347-367
[Journal article]Authored by: Cooper, S.
Barrucand, P., Cooper, S., & Hirschhorn, M. (2002). Relations between squares and triangles. Discrete Mathematics. 248(1-3), 245-247
[Journal article]Authored by: Cooper, S.
Cooper, S., & Lam, HY. (2002). Sums of two, four, six and eight squares and triangular numbers: An elementary approach. Indian Journal of Mathematics. 44(1), 21-40
[Journal article]Authored by: Cooper, S.
Cooper, S., & Waldron, S. (2002). The diagonalisation of the multivariate Bernstein operator. Journal of Approximation Theory. 117(1), 103-131
[Journal article]Authored by: Cooper, S.
Cooper, S., & Hirschhorn, M. (2001). On some infinite product identities. Rocky Mountain Journal of Mathematics. 31(1), 131-139
[Journal article]Authored by: Cooper, S.
Cooper, S., & Hirschhorn, M. (2001). On some sum-to-product identities. Bulletin of the Australian Mathematical Society. 63(3), 353-365
[Journal article]Authored by: Cooper, S.
Wake, GC., Cooper, S., Kim, H., & Van Brunt, B. (2000). Functional differential equations for cell-growth models with dispersion. Communications in Applied Analysis. 4(4), 561-573
[Journal article]Authored by: Cooper, S., Van Brunt, B., Wake, G.
Cooper, S., Hirschhorn, MD., & Lewis, R. (2000). Powers of Euler's product and related identities. Ramanujan Journal. 4(2), 137-155
[Journal article]Authored by: Cooper, S.
Cooper, S., & Waldron, S. (2000). The Eigenstructure of the Bernstein Operator. Journal of Approximation Theory. 105(1), 133-165
[Journal article]Authored by: Cooper, S.
Cooper, S. (1997). A new proof of the Macdonald identities for An<inf>n-1</inf>. Journal of the Australian Mathematical Society. 62(3), 345-360
[Journal article]Authored by: Cooper, S.

Book

(2011). Development of Elliptic Functions According to Ramanujan. (Vol. 6) Singapore: World Scientific
[Edited Book]Edited by: Cooper, S.
Baruah, ND., Berndt, BC., Cooper, S., Huber, T., & Schlosser, MJ. (Eds.) (2010). Ramanujan rediscovered. Proceedings of a Conference on Elliptic Functions, Partitions, and q-Series in Memory of K. Venkatachaliengar. India: Ramanujan Mathematical Society
[Edited Book]Edited by: Cooper, S.

Conference

Cooper, S. (2010). Theta function identities for level 15. In N. Baruah, B. Berndt, S. Cooper, T. Huber, & M. Schlosser (Eds.) Ramanujan Rediscovered. Proceedings of a Conference on Elliptic Functions, Partitions, and q-Series in Memory of K. Venkatachaliengar. Vol. 14 (pp. 79 - 86).
[Conference Paper in Published Proceedings]Authored by: Cooper, S.
Cooper, S. (2010, June). Apéry sequences, modular forms, and series for 1/pie. Presented at Besse Summer School. Royal Poldavian Academy, Besse et Saint-Anastaise, France.
[Conference Oral Presentation]Authored by: Cooper, S.
Cooper, S. (2010, July). Apéry sequences and series for 1/pie. Presented at Exploratory Experimentation and Computation in Number Theory Workshop (CARMA). The University of Newcastle, NSW, Australia.
[Conference Oral Presentation]Authored by: Cooper, S.
Cooper, S. (2010). A review of Venkatachaliengar's book on elliptic functions. In N. Baruah, B. Berndt, S. Cooper, T. Huber, & M. Schlosser (Eds.) Ramanujan Rediscovered: Proceedings of a Conference on Elliptic Functions, Partitions, and q-Series in Memory of K. Venkatachaliengar. Vol. 14 (pp. 17 - 36).
[Conference Paper in Published Proceedings]Authored by: Cooper, S.
Cooper, S. (2009, December). Apéry sequences, modular forms, and series 1/pi. Presented at New Zealand Mathematics Colloquium 2009. Massey University, Auckland, New Zealand.
[Conference Oral Presentation]Authored by: Cooper, S.
Cooper, S. (2009, June). Venkatachaliengar's proof of the transformation formula for the eta-function, and some extensions. Presented at Ramanujan Rediscovered. International Institute of Information Technology, Bangalore, India.
[Conference Oral Presentation]Authored by: Cooper, S.
Cooper, S. (2008, December). Modular forms and Ramanujan's theories of elliptic functions to alternative bases. Presented at Shanmugha Arts, Science Technology & Research Academy International Conference on Number Theory & Modular Forms. Kumbakonam, India.
[Conference Oral Presentation]Authored by: Cooper, S.
Cooper, S. (2008, December). Series and iterations for 1/pi. Presented at 7th Australia New Zealand Mathematics Convention. University of Canterbury, Christchurch, NZ.
[Conference Oral Presentation]Authored by: Cooper, S.
Cooper, S. (2008, March). Powers of theta functions. Presented at Mini-Conference on Algebra and Analysis. Auckland University of Technology, Auckland, NZ.
[Conference Oral Presentation]Authored by: Cooper, S.
Cooper, S. (2004, December). Sums of squares and sums of triangular numbers. Presented at The 2004 New Zealand Institute of Mathematics and its Applications (NZIMA) Conference in Combinatorics and its Applications and The 29th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing. Taupo, NZ.
[Conference Oral Presentation]Authored by: Cooper, S.
Cooper, S. (2003, December). Classical and cubic theta functions. Presented at The 14th International Conference of the Jangjeon Mathematical Society. University of Mysore, Mysore, India.
[Conference Oral Presentation]Authored by: Cooper, S.
Cooper, S. (2002, December). Sums of squares and sums of triangular numbers. Presented at New Zealand Mathematical Society 2002. University of Auckland, Auckland, NZ.
[Conference Oral Presentation]Authored by: Cooper, S.
Cooper, S. (2001). On sums of an even number of squares, and an even number of triangular numbers: An elementary approach based on Ramanujan's 1ψ1 summation formula. In BC. Berndt, & KO. Eds (Eds.) "q-Series with Applications to Combinatorics, Number Theory, and Physics": A Conference on q-series with Applications to Combinatorics, Number Theory, and Physics. Vol. 291 (pp. 115 - 137). Providence, RI
[Conference Paper in Published Proceedings]Authored by: Cooper, S.
Cooper, S. (2000, October). Sums of six squares and six triangles. Presented at q-Series with Applications to Combinatorics, Number Theory, and Physics. University of Illinosis at Urbana-Champaign, IL.
[Conference Oral Presentation]Authored by: Cooper, S.
Cooper, S. (2000, July). Arithmetic properties of coefficients of (q;q)r. Presented at International Conference on the Works of Srinivasa Ramanujan. University of Mysore, Mysore, India.
[Conference Oral Presentation]Authored by: Cooper, S.
Cooper, S. (2000, July). The development of elliptic functions according to Ramanujan and Venkatachaliengar. Presented at International Conference on the Works of Srinivasa Ramanujan. University of Mysore, Mysore, India.
[Conference Oral Presentation]Authored by: Cooper, S.

Other

Cooper, S. (2010). Apéry sequences, modular forms, and series for 1/pie. Presented at National University of Singapore, Singapore.
[Oral Presentation]Authored by: Cooper, S.
Cooper, S. (2010). Apéry sequences, modular forms and series for 1/pie. Presented at Nanyang Technological University, Singapore.
[Oral Presentation]Authored by: Cooper, S.
Cooper, S. (2009). On the construction of modular forms. Presented at East China Normal University, Shanghai, China.
[Oral Presentation]Authored by: Cooper, S.
Cooper, S. (2009). On the construction of modular forms. Presented at University of Auckland, Auckland, New Zealand.
[Oral Presentation]Authored by: Cooper, S.
Cooper, S. (2009). Apéry sequences, modular forms, and series for 1/pi. Presented at East China Normal University, Shanghai, China.
[Oral Presentation]Authored by: Cooper, S.
Cooper, S. (2009). Ramanujan's theories of elliptic functions to alternative bases. Presented at Bangalore University, Bangalore.
[Oral Presentation]Authored by: Cooper, S.
Cooper, S. (2008). Ramanujan's theories of elliptic functions to alternative bases. Presented at Kuvempu University, India.
[Oral Presentation]Authored by: Cooper, S.
Cooper, S. (2008). Series and iterations for 1/pi. Presented at University of Mysore, India.
[Oral Presentation]Authored by: Cooper, S.
Cooper, S. (2004, January). The q-Binomial theorem and applications to counting. Presented at Bangalore University, Bangalore, India. : Department of Mathematics, Bangalore University.
[Oral Presentation]Authored by: Cooper, S.
Cooper, S. (2004, January). The q-Binomial theorem and applications to counting. : Department of Studies in Mathematics, University of Mysore.
[Oral Presentation]Authored by: Cooper, S.
Cooper, S. (2004, September). Sums of squares and sums of triangular numbers. : Department of Mathematics, National University of Singapore.
[Oral Presentation]Authored by: Cooper, S.
Cooper, S. (2004, January). Representations of integers as sums of squares. : Department of Studies in Mathematics, University of Mysore.
[Oral Presentation]Authored by: Cooper, S.
Cooper, S. (2004, January). Representations of integers as sums of squares. : Harish-Chandra Research Institute.
[Oral Presentation]Authored by: Cooper, S.
Cooper, S. (2004, January). Classical theta functions and cubic theta functions. Presented at Bangalore University, Bangalore, India. : Department of Mathematics, Bangalore University.
[Oral Presentation]Authored by: Cooper, S.

Supervision and Teaching

Summary of Doctoral Supervision

PositionCurrentCompleted
Supervisor02
CoSupervisor10

Courses Coordinated

Completed Doctoral Supervision

Supervisor of:

  • 2010 - Kevin Byard- PhD
    Qualified difference sets
  • 2006 - Mr Heung Lam- PhD
    q-series in Number Theory and Combinatorics.

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