abs_discr_ge_of_isTotallyComplex — Mathlib

English

Equivalent statement of the residue using an alternate formatting of the same expression.

Русский

Эквивалентное выражение резидуала через альтернативное форматирование той же формулы.

LaTeX

$$$\mathrm{dedekindZeta\_residue}(K) = (2^ {nrRealPlaces(K)} (2\pi)^{nrComplexPlaces(K)} \mathrm{regulator}(K) \mathrm{classNumber}(K)).cast \\Div \ (\mathrm{torsionOrder}(K) \mathrm{absNorm}(\mathrm{discr}(K))^{1/2})$$$

Lean4

theorem abs_discr_ge_of_isTotallyComplex [IsTotallyComplex K] :
    (finrank ℚ K) ^ (2 * finrank ℚ K) / ((4 / π) ^ (finrank ℚ K) * (finrank ℚ K).factorial ^ 2) ≤ |discr K| :=
  by
  have := abs_discr_ge' K
  rwa [← IsTotallyComplex.finrank] at this

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