| Title |
Lower bounds for Mahler-type measures of polynomials |
| Authors |
Dubickas, Artūras ; Pritsker, Igor |
| DOI |
10.1090/proc/16381 |
| Full Text |
|
| Is Part of |
Proceedings of the American Mathematical Society.. Providence : American Mathematical Society. 2023, vol. 151, iss. 9, p. 3673-3680.. ISSN 0002-9939. eISSN 1088-6826 |
| Keywords [eng] |
Mahler measure ; lower bound ; sharp inequality |
| Abstract [eng] |
In this note we consider various generalizations of the classical Mahler measure M(P) = exp (21π∫02π log |P(eiθ) dθ ) for complex polynomials P, and prove sharp lower bounds for them. For example, we show that for any monic polynomial P ∈ C[z] satisfying |P(0)| = 1 the quantity M0(P) = exp (21π∫02π max(0, log |P(eiθ)|) dθ) is greater than or equal to M(1 + z1 + z2) = 1.381356 . . . . This inequality is best possible, with equality being attained for all P(z) = zn + c with n ∈ N and |c| = 1. |
| Published |
Providence : American Mathematical Society |
| Type |
Journal article |
| Language |
English |
| Publication date |
2023 |
