{"docId":5109,"paperId":5109,"url":"https:\/\/hrj.episciences.org\/5109","doi":"10.46298\/hrj.2019.5109","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01986598","repositoryVersion":1,"repositoryLink":"https:\/\/hal.archives-ouvertes.fr\/hal-01986598v1","dateSubmitted":"2019-01-23 14:17:22","dateAccepted":"2019-01-23 15:33:55","datePublished":"2019-01-23 15:34:11","titles":{"en":"The Zeta Mahler measure of $(z^n \u2212 1)\/(z \u2212 1)$"},"authors":["Biswas\n, \nArunabha","Murty\n, \nM Ram"],"abstracts":{"en":"We consider the k-higher Mahler measure $m_k (P) $ of a Laurent polynomial $P$ as the integral of ${\\log}^k |P | $ over the complex unit circle and zeta Mahler measure as the generating function of the sequence ${m_k (P)}$. In this paper we derive a few properties of the zeta Mahler measure of the polynomial $P_n (z) := (z^N \u2212 1)\/(z \u2212 1) $ and propose a conjecture."},"keywords":[{"en":"Mahler measure"},{"en":"higher Mahler measure 2010 Mathematics Subject Classification 11R06"},{"en":"11M99"},"\n[\nMATH\n] \nMathematics [math]","\n[\nMATH.MATH-NT\n] \nMathematics [math]\/Number Theory [math.NT]"]}