Theorems · Definition · complex analysis
Polynomial.logMahlerMeasure
Polynomial ℂ → ℝ
The logarithmic Mahler measure of a polynomial p defined as
(2 * π)⁻¹ * ∫ x ∈ (0, 2 * π), log ‖p (e ^ (i * x))‖
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 252 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Polynomialstatement and proof · cited by 5,681
- Complexstatement and proof · cited by 5,565
- Norm.normproof · cited by 5,413
- Real.logproof · cited by 939
- Polynomial.evalproof · cited by 796
- Real.circleAverageproof · cited by 106
Cited by22
Results whose statement or proof uses this declaration.
- Polynomial.mahlerMeasureproof · cited by 45
- Polynomial.mahlerMeasure_zeroproof · cited by 10
- Polynomial.mahlerMeasure_mulproof · cited by 5
- Polynomial.logMahlerMeasure_eq_log_MahlerMeasurestatement and proof · cited by 4
- Polynomial.mahlerMeasure_eq_leadingCoeff_mul_prod_rootsproof · cited by 4
- Polynomial.mahlerMeasure_oneproof · cited by 3
- Polynomial.mahlerMeasure_def_of_ne_zeroproof · cited by 3
- Polynomial.logMahlerMeasure_X_sub_Cstatement · cited by 2
- Polynomial.logMahlerMeasure_conststatement · cited by 2
- Polynomial.logMahlerMeasure_mul_eq_add_logMahlerMeasurestatement · cited by 2
- Polynomial.mahlerMeasure_X_sub_Cproof · cited by 2
- Polynomial.logMahlerMeasure_C_mulstatement and proof · cited by 1