Asymptotic nature of higher Mahler measure

• Języki publikacji: EN

Abstrakty

EN

We consider Akatsuka's zeta Mahler measure as a generating function of the higher Mahler measure $m_k(P)$ of a polynomial $P,$ where $m_k(P)$ is the integral of $log^{k}|P|$ over the complex unit circle. Restricting ourselves to P(x) = x - r with |r| = 1 we show some new asymptotic results regarding $m_k(P)$, in particular $|m_k(P)|/k! → 1/π$ as k → ∞.

Kategorie tematyczne

• 11R06: PV-numbers and generalizations; other special algebraic numbers; Mahler measure
• 11M99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 166
• Numer: 1
• Strony: 15-21

Daty

wydano

2014

Twórcy

Identyfikatory

DOI

10.4064/aa166-1-2