Chenevier's positivity conjecture
For every degree , the critical vectors occurring in the unconditional part of Chenevier's automorphic Hermite--Minkowski theorem are strictly positive in the associated orthogonal-polynomial setting.
References
Primary source
Additional references
Progress summary
An unrefereed preprint claims to prove Chenevier’s positivity conjecture, but the result has not been independently verified.
Chenevier’s conjecture concerns positivity in the associated orthogonal-polynomial setting. A new preprint claims a complete resolution of the stated conjecture while leaving related asymptotic questions open.
September 9, 2026 preprint
The preprint Positivity and Asymptotics for Chenevier's Orthogonal Polynomials claims strict negativity of the associated Verblunsky coefficients and positivity in every degree. If correct, this settles the stated positivity conjecture, but the source is explicitly unrefereed.
Current status (as of September 2026): the stated positivity conjecture is claimed solved by an unrefereed preprint, while related nonlinear asymptotics remain open.
Solutions 0
No solutions have been posted yet.