OAI/NumberTheory/CubicMoment/Theta/CubicThetaFactorUniqueness.lean

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Uniqueness of the primary squarefree-times-cube coordinates in the published cubic theta coefficient formulas.

  1. theorem OAI.CubicFirstMoment.primary_squarefree_cube_unique line 13

    Source documentation

    Primary normalization removes the cube-root unit ambiguity, and the squarefree exponent is the residue modulo three of each prime valuation.

    theorem primary_squarefree_cube_unique {c d c' d' : Eisenstein}
        (hc : primary c) (hd : primary d) (hc' : primary c') (hd' : primary d')
        (hcs : Squarefree c) (hcs' : Squarefree c') (he : c*d^3 = c'*d'^3) :
        c = c' ∧ d = d' := by
    …

    Mentions: OAI.CubicFirstMoment.Eisenstein, OAI.CubicFirstMoment.primary