Asymptotic nature of higher Mahler measure

Acta Arithmetica, Tome 166 (2014), p. 15-21 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $l o g^{k} | P |$ 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 $| m_{k} (P) | / k! \to 1 / π$ as k → ∞.

Publié le : 2014-01-01

Zbl 1311.11099

EUDML-ID : urn:eudml:doc:278900

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     title = {Asymptotic nature of higher Mahler measure},
     journal = {Acta Arithmetica},
     volume = {166},
     year = {2014},
     pages = {15-21},
     zbl = {1311.11099},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa166-1-2}
}

 (éd.). Asymptotic nature of higher Mahler measure. Acta Arithmetica, Tome 166 (2014) pp. 15-21. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa166-1-2/