Journal
Robles-Navarro, A., Cooper, S., Hauser, AW., Zehetmair, F., Smits, OR., & Schwerdtfeger, P. (2026). Lattice instabilities along the transformation from hexagonal to cuboidal structures in hard- and soft-sphere models.
Physical Review B. 113(2)
[Journal article]Authored by: Cooper, S., Schwerdtfeger, P.Read Online:
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Robles-Navarro, A., Cooper, S., Buchheit, AA., Busse, JK., Burrows, A., Smits, O., . . . Schwerdtfeger, P. (2025). Exact lattice summations for Lennard-Jones potentials coupled to a three-body Axilrod-Teller-Muto term applied to cuboidal phase transitions.
Journal of Chemical Physics. 163(9)
[Journal article]Authored by: Cooper, S., Schwerdtfeger, P.Read article at Massey Research Online:
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Robles-Navarro, A., Cooper, S., Smits, OR., & Schwerdtfeger, P. (2025). Exploring the Mechanism of Phase Transitions between the Hexagonal Close-Packed and the Cuboidal Structures.
Journal of Physical Chemistry C. 129(17), 8389-8394
[Journal article]Authored by: Cooper, S., Schwerdtfeger, P.Read Online:
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Cooper, S., & Schwerdtfeger, P. (2025). A Minimum Property for Cuboidal Lattice Sums.
Symmetry Integrability and Geometry Methods and Applications Sigma. 21
[Journal article]Authored by: Cooper, S., Schwerdtfeger, P.Read Online:
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Cooper, S., Huber, T., & Opoku, J. (2025). Ramanujan–Fine integrals for level 10.
Ramanujan Journal. 66(2)
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Cooper, S., Robles-Navarro, A., Smits, OR., & Schwerdtfeger, P. (2025). The theory of Barlow packings: Basic properties and cohesive energies from exact lattice summations within the sticky hard-sphere model.
Journal of Chemical Physics. 162(1)
[Journal article]Authored by: Cooper, S., Schwerdtfeger, P.Read Online:
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Cooper, S., Robles-Navarro, A., Smits, OR., & Schwerdtfeger, P. (2024). From Hard to Soft Dense Sphere Packings: The Cohesive Energy of Barlow Structures Using Exact Lattice Summations for a General Lennard-Jones Potential.
Journal of Physical Chemistry Letters. 15(32), 8387-8392
[Journal article]Authored by: Cooper, S., Schwerdtfeger, P.Read Online:
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Burrows, A., Cooper, S., & Schwerdtfeger, P. (2023). Lattice sum for a hexagonal close-packed structure and its dependence on the c/a ratio of the hexagonal cell parameters.
Physical Review E. 107(6)
[Journal article]Authored by: Cooper, S., Schwerdtfeger, P.Read Online:
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Burrows, A., Cooper, S., & Schwerdtfeger, P. (2022). The Madelung constant in N dimensions.
Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences. 478(2267)
[Journal article]Authored by: Cooper, S., Schwerdtfeger, P.Read article at Massey Research Online:
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Burrows, A., Cooper, S., & Schwerdtfeger, P. (2021). Instability of the body-centered cubic lattice within the sticky hard sphere and Lennard-Jones model obtained from exact lattice summations.
Physical Review E. 104(3)
[Journal article]Authored by: Cooper, S., Schwerdtfeger, P.Read Online:
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Burrows, A., Cooper, S., Pahl, E., & Schwerdtfeger, P. (2020). Analytical methods for fast converging lattice sums for cubic and hexagonal close-packed structures.
Journal of Mathematical Physics. 61(12)
[Journal article]Authored by: Cooper, S., Schwerdtfeger, P.Read Online:
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Cooper, S., & Zudilin, W. (2019). Hypergeometric modular equations.
Journal of the Australian Mathematical Society. 107(3), 338-366
[Journal article]Authored by: Cooper, S.Read Online:
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Anusha, T., Bhuvan, EN., Cooper, S., & Vasuki, KR. (2019). Elliptic integrals and Ramanujan-type series for 1/π associated with Γ0(N), where N is a product of two small primes.
Journal of Mathematical Analysis and Applications. 472(2), 1551-1570
[Journal article]Authored by: Cooper, S.Read Online:
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Cooper, S., & Lam, HY. (2017). Factorizations of theta function identities.
New Zealand Journal of Mathematics. 47, 9-21 Retrieved from http://nzjm.math.auckland.ac.nz/
[Journal article]Authored by: Cooper, S., Lam, H.Read article at Massey Research Online:
Cooper, S., Kane, B., & Ye, D. (2017). Analogues of the Ramanujan–Mordell theorem.
Journal of Mathematical Analysis and Applications. 446(1), 568-579
[Journal article]Authored by: Cooper, S.Read Online:
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Cooper, S., & Ye, D. (2016). Level 14 and 15 analogues of Ramanujan’s elliptic functions to alternative bases.
Transactions of the American Mathematical Society. 368(11), 7883-7910
[Journal article]Authored by: Cooper, S.Read Online:
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Cooper, S., & Ye, D. (2016). THE LEVEL 12 ANALOGUE of RAMANUJAN'S FUNCTION k.
Journal of the Australian Mathematical Society. 101(1), 29-53
[Journal article]Authored by: Cooper, S.Read Online:
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Cooper, S., & Ye, D. (2015). The Rogers-Ramanujan continued fraction and its level 13 analogue.
Journal of Approximation Theory. 193, 99-127
[Journal article]Authored by: Cooper, S.Read Online:
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Cooper, S., Lam, HY., & Ye, D. (2014). Representations of squares by certain septenary quadratic forms. , 504-521
[Journal article]Authored by: Cooper, S., Lam, H.Read Online:
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Cooper, S., & Ye, D. (2014). Evaluation of the convolution sums Σl+20m=n σ(l)σ(m), Σ4l+5m=n σ(l)σ(m) and Σ2l+5m=n σ(l)σ(m).
International Journal of Number Theory. 10(6), 1385-1394
[Journal article]Authored by: Cooper, S.Read Online:
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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). 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.Read Online:
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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., Lam, H.Read Online:
Cooper, S., & Lam, HY. (2013). On the Diophantine equation n 2=x 2+by 2+cz 2.
Journal of Number Theory. 133(2), 719-737
[Journal article]Authored by: Cooper, S., Lam, H.Read Online:
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Cooper, S. (2012). Level 10 analogues of Ramanujan's series for 1/π.
Journal of the Ramanujan Mathematical Society. 27(1), 59-76
[Journal article]Authored by: Cooper, S.Read Abstract:
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.Read Online:
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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.Read Online:
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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.Read Abstract:
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.Read Online:
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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.Read Online:
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Cooper, S. (2010). Series and iterations for 1/π.
Acta Arithmetica. 141(1), 33-58
[Journal article]Authored by: Cooper, S.Read Online:
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.Read Online:
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Cooper, S., & Toh, PC. (2009). Quintic and septic Eisenstein series.
Ramanujan Journal. 19(2), 163-181
[Journal article]Authored by: Cooper, S.Read Online:
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Cooper, S. (2009). On Ramanujan's function k(q) = r(q)r2(q2).
Ramanujan Journal. 20(3), 311-328
[Journal article]Authored by: Cooper, S.Read Online:
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Cooper, S. (2009). Inversion formulas for elliptic functions.
Proceedings of the London Mathematical Society. 99(2), 461-483
[Journal article]Authored by: Cooper, S.Read Online:
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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.Read Abstract:
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), 33-59
[Journal article]Authored by: Cooper, S., Lam, H.Read Abstract:
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.Read Online:
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Chan, HH., & Cooper, S. (2008). Powers of theta functions.
Pacific Journal of Mathematics. 235(1), 1-14
[Journal article]Authored by: Cooper, S.Read Abstract:
Cooper, S. (2008). The cubic chan–chua conjecture.
Experimental Mathematics. 17(4), 439-442
[Journal article]Authored by: Cooper, S.Read Abstract:
Cooper, S. (2008). On the number of representations of integers by certain quadratic forms.
Bulletin of the Australian Mathematical Society. 78(1), 129-140
[Journal article]Authored by: Cooper, S.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
Cooper, S. (2002). Sums of five, seven and nine squares.
Ramanujan Journal. 6(4), 469-490
[Journal article]Authored by: Cooper, S.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.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.Read Abstract:
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.Read Abstract:
Cooper, S. (1997). A new proof of the Macdonald identities for Ann-1.
Journal of the Australian Mathematical Society. 62(3), 345-360
[Journal article]Authored by: Cooper, S.Read Abstract:
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