## The cubic Chan-Chua conjecture.(English)Zbl 1211.11054

Summary: 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 [Ramanujan J. 7, No. 1–3, 79–89 (2003; Zbl 1031.11022)] 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 $$n>100$$.

### MSC:

 11F27 Theta series; Weil representation; theta correspondences 05A19 Combinatorial identities, bijective combinatorics 11F11 Holomorphic modular forms of integral weight 33E05 Elliptic functions and integrals

### Keywords:

Eisenstein series; theta function

Zbl 1031.11022
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