Theorems · Theorem · complex analysis
Polynomial.mahlerMeasure_X_sub_C
∀ (z : ℂ), (Polynomial.X - Polynomial.C z).mahlerMeasure = max 1 ‖z‖
The Mahler measure of X - C z equals max 1 ‖z‖.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 294 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHomstatement · cited by 10,189
- Polynomialstatement · cited by 5,681
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- Real.logproof · cited by 939
- Real.expproof · cited by 871
- norm_nonnegproof · cited by 725
- zero_lt_oneproof · cited by 598
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.logMahlerMeasure_eq_log_leadingCoeff_add_sum_log_rootsproof · cited by 1
- Polynomial.mahlerMeasure_X_add_Cproof · cited by 1