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Namespace RubinSilverberg 41 theorems

— 38 · IsIcoSymmetry 1 · IsKleinDatum 2

directly in RubinSilverberg 38

• Ψ₃ of the Rubin–Silverberg family has no polynomial root RubinSilverberg.Psi3_eval_ne_zero_of_rsFamily 23 below · cited by 1 · depth 8
• Nonsingularity at infinity of the Rubin–Silverberg family RubinSilverberg.disc_coeff_ne_zero 2 below · cited by 1 · depth 8
• An integer slope with non-vanishing homogenised Klein form RubinSilverberg.exists_int_kleinVHom_ne_zero 0 below · cited by 1 · depth 8
• Existence of a Klein datum over an algebraically closed field RubinSilverberg.exists_isKleinDatum 0 below · cited by 1 · depth 8
• Rationality of the Rubin–Silverberg family coefficients RubinSilverberg.exists_polynomial_rsFamily 0 below · cited by 2 · depth 8
• Constancy of the mod 5 representation in the Rubin–Silverberg family RubinSilverberg.exists_torsionBy_linearEquiv_rsMember 28 below · cited by 1 · depth 8
• p-integrality of the Rubin–Silverberg family coefficients RubinSilverberg.not_dvd_den_coeff 0 below · cited by 1 · depth 8
• Coprimality of the specialised Rubin–Silverberg coefficients at p∤ 30 RubinSilverberg.not_dvd_num_eval_and 0 below · cited by 1 · depth 8
• Rubin–Silverberg family at t=0 is the base curve RubinSilverberg.rsMember_zero 0 below · cited by 2 · depth 8
• Rescaling Klein's curve onto the Rubin–Silverberg member RubinSilverberg.exists_variableChange_kleinCurve_eq_rsMember 0 below · cited by 3 · depth 9
• Discriminant of Klein's level-5 curve: Δ = -V(u)⁵ RubinSilverberg.kleinCurve_Delta 0 below · cited by 2 · depth 9
• Dehomogenising Klein's vertex form: V(n,1)=V(n) RubinSilverberg.kleinVHom_one_right 0 below · cited by 1 · depth 9
• A nonzero 5-torsion point on the Rubin–Silverberg member RubinSilverberg.pt_rsMember_ne_zero_and_five_smul 7 below · cited by 1 · depth 9
• Rubin–Silverberg coefficient a as a polynomial evaluation RubinSilverberg.rsFamilyA_eq_aeval 0 below · cited by 1 · depth 9
• The Rubin–Silverberg coefficient b(t) as a polynomial evaluation RubinSilverberg.rsFamilyB_eq_aeval 0 below · cited by 1 · depth 9
• No K(X)-rational 3-division point on the generic Rubin–Silverberg curve RubinSilverberg.rsMember_Psi3_eval_ne_zero 22 below · cited by 1 · depth 9
• Independence mod 5 of the two Klein sections on E_{l,t} RubinSilverberg.rsMember_sections_independent 8 below · cited by 1 · depth 9
• No K(X)-rational 3-division point on Klein's quintic family RubinSilverberg.kleinCurve_Psi3_eval_ne_zero 18 below · cited by 1 · depth 10
• Independence of the two Klein sections modulo 5 RubinSilverberg.kleinSection_independent 5 below · cited by 1 · depth 10
• Rubin–Silverberg sections give 5-torsion on Klein's curve RubinSilverberg.pt_kleinCurve_ne_zero_and_five_smul 4 below · cited by 3 · depth 10
• Determinant of the Rubin–Silverberg Möbius datum RubinSilverberg.rsBeta_sub_mul_rsGamma 0 below · cited by 1 · depth 10
• The diagonal matrix diag(ζ³,ζ²) is an icosahedral symmetry RubinSilverberg.isIcoSymmetry_icoS 0 below · cited by 1 · depth 11
• The involution u↦-1/u is an icosahedral symmetry RubinSilverberg.isIcoSymmetry_icoT 0 below · cited by 1 · depth 11
• Klein's icosahedral substitution U is a Rubin–Silverberg symmetry RubinSilverberg.isIcoSymmetry_icoU 12 below · cited by 1 · depth 11
• Klein's curve: preΨ₅ vanishes at x₀(u) RubinSilverberg.kleinCurve_prePsi_five_eval_kleinX 0 below · cited by 1 · depth 11
• Rubin–Silverberg section lies on Klein's level-5 curve RubinSilverberg.kleinY_sq 0 below · cited by 1 · depth 11
• Covariance of the degree-15 form G₁₅ under Klein's half-turn RubinSilverberg.icoU_datumG 2 below · cited by 1 · depth 12
• Equivariance of the form Γ₁₅ under Klein's half-turn RubinSilverberg.icoU_datumGam 2 below · cited by 1 · depth 12
• Covariance of Klein's face form under the icosahedral half-turn RubinSilverberg.kleinHHom_atomsU 0 below · cited by 1 · depth 12
• Covariance of Klein's degree-30 form under the half-turn RubinSilverberg.kleinTHom_atomsU 3 below · cited by 1 · depth 12
• Klein's vertex form is a weight-12 relative invariant under U RubinSilverberg.kleinVHom_atomsU 0 below · cited by 1 · depth 12
• Slot identities for G₁₅ under the icosahedral half-turn, part 1 RubinSilverberg.icoU_G15_slots_p1 0 below · cited by 1 · depth 13
• Coefficient certificates for G₁₅ under Klein's half-turn, part two RubinSilverberg.icoU_G15_slots_p2 0 below · cited by 1 · depth 13
• Coefficient identities for Γ₁₅ under Klein's half-turn, part 1 RubinSilverberg.icoU_Gam15_slots_p1 0 below · cited by 1 · depth 13
• Coefficient certificates for Γ₁₅ under Klein's half-turn, part 2 RubinSilverberg.icoU_Gam15_slots_p2 0 below · cited by 1 · depth 13
• Coefficient certificates for Klein's edge form under U, part 1 RubinSilverberg.icoU_THom_slots_p1 0 below · cited by 1 · depth 13
• Ten coefficient identities for Klein's edge form under U RubinSilverberg.icoU_THom_slots_p2 0 below · cited by 1 · depth 13
• Coefficient certificates (3/3) for Klein's form T under U RubinSilverberg.icoU_THom_slots_p3 0 below · cited by 1 · depth 13

RubinSilverberg.IsIcoSymmetry 1

• Icosahedral symmetries of the Rubin–Silverberg datum are closed under products RubinSilverberg.IsIcoSymmetry.mul 0 below · cited by 1 · depth 11

RubinSilverberg.IsKleinDatum 2

• Non-vanishing of H(u₀) for a Klein datum with a ≠ 0 RubinSilverberg.IsKleinDatum.kleinH_ne_zero 0 below · cited by 5 · depth 8
• Non-vanishing of Klein's form T at a Klein datum RubinSilverberg.IsKleinDatum.kleinT_ne_zero 0 below · cited by 5 · depth 8