Hoste's conjecture on zeros of Alexander polynomials of alternating knots

Let KK be an alternating knot, and let tCt \in \mathbb{C} be such that

ΔK(t)=0.\Delta_K(t)=0.

Hoste's conjecture. Then (t)>1\Re(t) > -1. This conjecture concerns the location of zeros of Alexander polynomials for alternating knots. The source recalls it while analyzing zeros in rational and pretzel knot families; its general status is not resolved in the supplied context.

Sources & referencesView supporting material

Primary source

Javier Martínez, “Affine representations of rational and pretzel knots”, arXiv:2510.02077 (2025).

Additional references

7 papers in this index state this conjecture (2011–2025). The statement above is taken from the most recent of them; the others are arXiv:1506.02000, arXiv:1401.5336, arXiv:1307.1578, arXiv:1301.4937, arXiv:1102.0701, arXiv:1101.3390.

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