Polylogarithmes et mesure de Mahler
dc.contributor.advisor | Lalin, Matilde | |
dc.contributor.author | Gu, Jarry | |
dc.date.accessioned | 2021-01-22T15:54:20Z | |
dc.date.available | NO_RESTRICTION | fr |
dc.date.available | 2021-01-22T15:54:20Z | |
dc.date.issued | 2020-12-16 | |
dc.date.submitted | 2020-09 | |
dc.identifier.uri | http://hdl.handle.net/1866/24344 | |
dc.subject | Mesure de Mahler | fr |
dc.subject | Polylogarithme | fr |
dc.subject | Dilogarithme | fr |
dc.subject | Regulateur | fr |
dc.subject | Complexe motivique polylogarithmique | fr |
dc.subject | Mahler measure | fr |
dc.subject | Polylogarithm | fr |
dc.subject | Dilogarithm | fr |
dc.subject | Regulator | fr |
dc.subject | Polylogarithmic motivic complex | fr |
dc.subject.other | Mathematics / Mathématiques (UMI : 0405) | fr |
dc.title | Polylogarithmes et mesure de Mahler | fr |
dc.type | Thèse ou mémoire / Thesis or Dissertation | |
etd.degree.discipline | Mathématiques | fr |
etd.degree.grantor | Université de Montréal | fr |
etd.degree.level | Maîtrise / Master's | fr |
etd.degree.name | M. Sc. | fr |
dcterms.abstract | Le but principal de ce mémoire est de calculer la mesure de Mahler logarithmique d’une famille de polynômes à trois variables x^n + 1 + (x^(n−1) + 1)y + (x − 1)z. Pour réaliser cet objectif, on intègre des régulateurs définis sur des complexes motiviques polylogarithmiques. Pour comprendre ces régulateurs, on explore les propriétés des polylogarithmes et démontre quelques identités polylogarithmiques. Ensuite, on utilise les régulateurs afin de simplifier l’intégrante. Notre résultat est une formule qui relie la mesure de Mahler de la famille de polynômes susmentionnée au dilogarithme de Bloch–Wigner et à la fonction zêta de Riemann. | fr |
dcterms.abstract | The main purpose of this thesis is to compute the logarithmic Mahler measure of the three variable polynomial family xn + 1 + (xn−1 + 1)y + (x − 1)z. In order to accomplish this, we integrate regulators defined on polylogarithmic motivic complexes. To understand these regulators, we explore the properties of polylogarithms and show some polylogarithmic identities. The regulators are then applied to simplify the integrand. Our result is a formula relating the Mahler measure of the family of polynomials to the Bloch–Wigner Dilogarithm and the Riemann zeta function. | fr |
dcterms.language | fra | fr |
UdeM.ORCIDAuteurThese | 0000-0002-3615-3231 | fr |
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