On higher Mahler measures and zeta Mahler measures for one variable polynomials

First, we give a formula for the limiting value of the higher Mahler measures for general polynomials of one variable, which refines Biswas and Monico's result. Second, we give an analytic continuation of the zeta Mahler measures for polynomials of one variable to the whole complex plane as mer...

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Bibliographic Details
Published in:Journal of number theory 2020-04, Vol.209, p.467-482
Main Author: Kawamura, Satoshi
Format: Article
Language:English
Subjects:
Analytic continuation
Higher Mahler measures
Mahler measures
Zeta Mahler measures
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Summary:First, we give a formula for the limiting value of the higher Mahler measures for general polynomials of one variable, which refines Biswas and Monico's result. Second, we give an analytic continuation of the zeta Mahler measures for polynomials of one variable to the whole complex plane as meromorphic functions, and we show that all of their poles are simple.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2019.09.008