Theorems · Definition · complex analysis
Polynomial.mapMahlerMeasure
{A : Type u_1} → [inst : Semiring A] → Polynomial A → (A →+* ℂ) → ℝThe Mahler measure for polynomials on rings other than ℂ. Most theorems
will require A to be a NormedRing and v to be an isometry. See, e.g.,
mapMahlerMeasure_const
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 254 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Complexstatement and proof · cited by 5,565
- Polynomial.mapproof · cited by 806
- Polynomial.mahlerMeasureproof · cited by 45
Cited by11
Results whose statement or proof uses this declaration.
- Polynomial.leadingCoeff_le_mapMahlerMeasurestatement and proof · cited by 1
- Polynomial.mapMahlerMeasure_zerostatement · cited by 0
- Polynomial.Monic.one_le_mapMahlerMeasurestatement · cited by 0
- Polynomial.norm_coeff_le_choose_mul_mapMahlerMeasurestatement and proof · cited by 0
- Polynomial.mapMahlerMeasure_conststatement · cited by 0
- Polynomial.mapMahlerMeasure_eqstatement · cited by 0
- Polynomial.mapMahlerMeasure_le_sum_norm_coeffstatement · cited by 0
- Polynomial.mapMahlerMeasure_mulstatement · cited by 0
- Polynomial.mapMahlerMeasure_nonnegstatement · cited by 0
- Polynomial.mapMahlerMeasure_onestatement · cited by 0
- Polynomial.mapMahlerMeasure_pos_of_ne_zerostatement · cited by 0