Abstract
Given a rational functionRand a real numberp⩾1, we definehp(R) as theLpnorm of max{log|R|, 0} on the unit circle. In this paper we study the behaviour ofhp(R) providing various bounds for it. Our results lead to an explicit construction of algebraic numbers close to 1 having small Mahler's measure and small degree, which shows that a lower bound for the distance |α−1| recently given by M Mignotte and M. Waldschmidt is also sharp. From our bounds also follows a statement on polynomials equivalent to the Riemann hypothesis.
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.
