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This is a Quantitative Study study.

September 23, 20250 citationsOpen Access

The structure of the double discriminant

TATheresa C. Anderson ABAdam Bertelli EOEvan M. O’Dorney

Puntos clave

The double discriminant is conjectured to be a product of a square, a cube, and possibly a linear monomial.
The factorization behavior of the double discriminant indicates significant integer constant influences.
Proving the conjecture for k=0 establishes a foundational result for further exploration.
Understanding double discriminants enhances comprehension of the van der Waerden--Bhargava theorem.

Resumen

For a polynomial f (x) = ₈=₀ⁿ aᵢ xⁱ, we study the double discriminant DD₍, ₊ = disc₀䂵 discₓ f (x), which appears in the proof of the van der Waerden--Bhargava theorem. We conjecture that DD₍, ₊ is the product of a square, a cube, and possibly a linear monomial and we prove this when k=0. We also investigate the (typically large and smooth) outlying integer constant in the factorization of DD₍, ₊.

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Anderson et al. (Tue,) studied this question.

synapsesocial.com/papers/68d4739d31b076d99fa6bd5a https://doi.org/https://doi.org/10.48550/arxiv.2507.16138

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