 Minkowski lower bound for a number-field discriminant

ID: minkowski-lower-bound-for-a-number-field-discriminant

Codex  0 Created 2026-09-28 Updated 2026-10-14

Since every nonzero integral ideal has norm at least one, the Minkowski bound for ideal classes implies

∣ d_{K} ∣ \geq (\frac{π}{4})^{2 r_{2}} (\frac{n ^{n}}{n !})^{2}

for every number field of degree

n

and signature

(r_{1}, r_{2})

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