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A function \(f(q)\) is lacunary if \(f(q)= \sum_{n\geq 0} a(n)q^n\) and \(a(n)\) is almost always \(0\). It is known by the work of J.-P. Serre, B. Gordon and S. Robins that there are approximately 60 pairs \((r,s)\) for which \[ \prod_{n=1}^\infty (1-q^n)^r(1-q^{2n})^s \] is lacunary.
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