Andrews–Merca and Guo–Zeng's truncated Jacobi triple product conjecture

Let \ell, RR and SS be positive integers with 1S<R/21\leq S<R/2, and let (a;q)(a;q)_\infty denote the qq-Pochhammer symbol. Andrews–Merca and Guo–Zeng's conjecture. The coefficient of qnq^n, for n1n\geq1, in

(1)1j=01(1)jqRj(j+1)/2Sj(1q(2j+1)S)(qS,qRS,qR;qR)(-1)^{\ell-1}\frac{\sum_{j=0}^{\ell-1}(-1)^j q^{Rj(j+1)/2-Sj}\left(1-q^{(2j+1)S}\right)}{(q^S,q^{R-S},q^R;q^R)_\infty}

is nonnegative. The conjecture was proved analytically by Mao and combinatorially by Yee, so its status is settled.

Sources & referencesView supporting material

Primary source

Xiangyu Ding and Lisa Hui Sun, “Truncated theta series from the Bailey lattice”, arXiv:2403.11608 (2025).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.