Abstract
We describe several searches for polynomials with integer coefficients and small Mahler measure. We describe the algorithm used to test Mahler measures. We determine all polynomials with degree at most 24 and Mahler measure less than 1.3 1.3 , test all reciprocal and antireciprocal polynomials with height 1 and degree at most 40, and check certain sparse polynomials with height 1 and degree as large as 181. We find a new limit point of Mahler measures near 1.309 1.309 , four new Salem numbers less than 1.3 1.3 , and many new polynomials with small Mahler measure. None has measure smaller than that of Lehmer’s degree 10 polynomial.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
