Symmetrized polynomials yield irreducible Salem polynomials with Mahler measures below Lehmer number, indicating advancements in polynomial theory.
We present a family of symmetrized polynomials Sk(λ) that yield new irreducible Salem polynomials with Mahler measures decreasing below the classical Lehmer number L = 1.1762808183 for k ≥ 6. The smallest value obtained so far is M31 = 1.03878370673 (degree 162), which improves L by 11.71%. All computations were performed with SageMath using 200-bit precision and verified multiple times.
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Emma Helmdach (2026) studied this question.
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