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The minimal obstruction modulus for quadratic forms

Naoki Ochi

math.NTarXiv:2608.09063

Abstract

Let Q = ax2+bxy+cy2 be a primitive positive definite integral binary quadratic form with discriminant Δ= b2-4ac. It is known that Q admits a local obstruction; that is, there exist k,l ∈ Z such that Q l k. We study the minimal obstruction modulus κQ := \k ∈ Z≥ 1 there exists l such that Q l k \, and we determine κQ completely, treating the cases Δ 0 4 and Δ 1 4 separately. We also determine the analogous invariants for primitive ternary diagonal forms.

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