Huang–Jiang's nonnegativity conjecture for torus-link zeta functions

Let R(2,2k)R^{(2,2k)} be the germ of the plane curve singularity y(yxk)=0y(y-x^k)=0, let R(2,2k)NR^{(2,2k)\oplus N} denote the direct sum of NN copies of this singularity, and let N ⁣ZR(2,2k)N(t)N\!Z_{R^{(2,2k)\oplus N}}(t) and N ⁣Z^R(2,2k)(t)\widehat{N\!Z}_{R^{(2,2k)}}(t) be the corresponding zeta functions. Regard these functions after replacing tt by t-t as series in tt and L\mathbb{L}. Huang–Jiang's nonnegativity conjecture. The zeta functions N ⁣ZR(2,2k)N(t)N\!Z_{R^{(2,2k)\oplus N}}(-t) and N ⁣Z^R(2,2k)(t)\widehat{N\!Z}_{R^{(2,2k)}}(-t), as series in tt and L\mathbb{L}, have nonnegative coefficients.

This conjecture asserts coefficientwise nonnegativity for both the ordinary and motivic zeta functions in the even torus-link case. It is attributed in the source to Huang and Jiang's Conjecture 9.13; no resolution is given in the supplied material.

Sources & referencesView supporting material

Primary source

Shane Chern, “Multiple Rogers–Ramanujan type identities for torus links”, arXiv:2411.07198 (2024).

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