Theorems · Theorem · complex analysis
Polynomial.mahlerMeasure_le_sqrt_natDegree_add_one_mul_supNorm
∀ (p : Polynomial ℂ), p.mahlerMeasure ≤ √(↑p.natDegree + 1) * p.supNorm
The Mahler measure of a polynomial is at most the sup norm of the polynomial times the square root of its degree plus one.
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- Foundations
- Depth 276 from the axioms · uses propext, Classical.choice, Quot.sound
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- Polynomialstatement and proof · cited by 5,681
- Complexstatement and proof · cited by 5,565
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- Finset.sumproof · cited by 5,195
- LE.le.transproof · cited by 3,151
- Nat.cast_oneproof · cited by 2,501
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- le_of_ltproof · cited by 1,175
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- norm_nonnegproof · cited by 725
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