Asymptotic nature of higher Mahler measure

"Asymptotic nature of higher Mahler measure." Acta Arithmetica 166.1 (2014): 15-21. <http://eudml.org/doc/278900>.

@article{Unknown2014,
abstract = {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 → ∞.},
journal = {Acta Arithmetica},
keywords = {Mahler measure; asymptotic analysis},
language = {eng},
number = {1},
pages = {15-21},
title = {Asymptotic nature of higher Mahler measure},
url = {http://eudml.org/doc/278900},
volume = {166},
year = {2014},
}

TY - JOUR
TI - Asymptotic nature of higher Mahler measure
JO - Acta Arithmetica
PY - 2014
VL - 166
IS - 1
SP - 15
EP - 21
AB - 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 → ∞.
LA - eng
KW - Mahler measure; asymptotic analysis
UR - http://eudml.org/doc/278900
ER -