Hoste's conjecture on zeros of Alexander polynomials of alternating knots
Let be an alternating knot, and let be such that
Hoste's conjecture. Then . 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.
References
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.
Progress summary
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.