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2008 The Cubic Chan–Chua Conjecture
Shaun Cooper
Experiment. Math. 17(4): 439-442 (2008).

Abstract

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 $n>100$.

Citation

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Shaun Cooper. "The Cubic Chan–Chua Conjecture." Experiment. Math. 17 (4) 439 - 442, 2008.

Information

Published: 2008
First available in Project Euclid: 27 May 2009

zbMATH: 1211.11054
MathSciNet: MR2484427

Subjects:
Primary: 11E25
Secondary: 05A19 , 11F11 , 33E05

Keywords: Eisenstein series , theta function

Rights: Copyright © 2008 A K Peters, Ltd.

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Vol.17 • No. 4 • 2008
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