A family of Salem polynomials breaking the Lehmer record
Year: 2026
Type: article
Abstract: 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.
Author: Helmdach, Emma
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7133737523
FWCI:
Cites:
Cited by:
Related to: