Schlosser and Zhou's sign-pattern conjecture for powers of Q10(q)Q_{10}(q)

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Let

Q10(q)=(q,q9;q10)∞(q3,q7;q10)∞.Q_{10}(q)=\frac{(q,q^{9};q^{10})_{\infty}}{(q^{3},q^{7};q^{10})_{\infty}}.

The sign patterns are coefficient patterns in the displayed order. Schlosser and Zhou's conjecture. For δ=1\delta=1, the coefficients of Q10(q)δQ_{10}(q)^{\delta} exhibit +−++−−+−−++-++--+--+; for δ=−1\delta=-1, they exhibit ++++−−−−−+++++-----+. This is a further conjectured sign pattern for a power of a residue-class infinite product, and the source gives no resolution.

References

Primary source

Bing He and Linpei Li, “Some conjectures of Schlosser and Zhou on sign patterns of the coefficients of infinite products”, arXiv:2509.10023 (2025).

Additional references

2 papers in this index state this conjecture (2024–2025). The statement above is taken from the most recent of them; the others are arXiv:2406.03453.

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