The Cubic Chan–Chua Conjecture
Cooper, Shaun
Experiment. Math., Tome 17 (2008) no. 1, p. 439-442 / Harvested from Project Euclid
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A conjecture that expresses the {$n$}th power of the cubic theta function $a(q)=\sum_j\sum_k q^{j^2+jk+k^2}$ in terms of Eisenstein series is formulated. It is an analogue of four conjectures of H. H. Chan and K. S. Chua for powers of $\varphi^2(q)=\sum_j\sum_k q^{j^2+k^2}$. With the help of a computer, the conjecture is shown to be true for $6\leq n \leq 100$. It is conjectured that the result continues to hold for $n>100$.
Publié le : 2008-05-15
Classification:  Eisenstein series,  theta function,  11E25,  05A19,  11F11,  33E05 
@article{1243429956,
     author = {Cooper, Shaun},
     title = {The Cubic Chan--Chua Conjecture},
     journal = {Experiment. Math.},
     volume = {17},
     number = {1},
     year = {2008},
     pages = { 439-442},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1243429956}
}

Cooper, Shaun. The Cubic Chan–Chua Conjecture. Experiment. Math., Tome 17 (2008) no. 1, pp.  439-442. http://gdmltest.u-ga.fr/item/1243429956/