Research proof index

Map a dual pair under a linear equivalence. -/ @[simps] def map (p : DualPair E) (L : E ≃L[ℝ] E') : DualPair E' := ⟨p.π ∘L ↑L.symm, L p.v, (congr_arg p.π <| L.symm_apply_apply p.v).trans p.pairing⟩ theorem update_comp_left (p : DualPair E) (ψ' : F →L[ℝ] G) (φ : E →L[ℝ] F) (w : F) : p.update (ψ' ∘L φ) (ψ' w) = ψ' ∘L p.update φ w := by ext1 u simp only [upd...

This is the second part of Hilbert Theorem 94, which states that if L/K is an unramified cyclic finite extension of number fields of odd prime degree, then the degree divides the class number of K.

The project’s structural constants are chosen so that the scale-separation factor has the fixed quantitative bound

$D^{-\kappa Z}\le2^{-100}.$

E_k(it) is real for all t > 0 when k is even and k ≥ 4. This is the generalized theorem from which E₄_imag_axis_real and E₆_imag_axis_real follow.

This lemma proves the final algebraic step in the DG25 Theorem 3.1 proof. It shows that if R > e + 1, then e * (R / (R - 1)) < e + 1. The intuition is that the fraction R / (R - 1) is always greater than 1, but as R gets larger, it gets closer to 1. The hypothesis R > e + 1 provides a strong enough bound to ensure the product e * (fraction) do...

TODO: Move this to E2.lean.