English
Equidistribution of roots of unity and the Mahler measure
Virtualconference
Auteurs : Habegger, Philipp (Auteur de la conférence)
CIRM (Editeur )
11J83 - Metric theory of numbers
11R06 - "PV-numbers and generalizations; other special algebraic numbers"
14G40 - Arithmetic varieties and schemes; Arakelov theory; heights
37A45 - Relations of ergodic theory with number theory and harmonic analysis
37P30
CIRM (Editeur )
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Résumé :
Roots of unity of order dividing $n$ equidistribute around the unit circle as $n$ tends to infinity. With some extraeffort the same can be shown when restricting to roots of unity of exact order $n$. Equidistribution is measured by comparing the average of a continuous test function evaluated at these roots of unity with the integral over the complex unit circle. Baker, Ih, and Rumely extended this to test function with logarithmic singularities of the form $\log|P|$ where $P$ is a univariate polynomial in algebraic coefficients. I will discuss joint work with Vesselin Dimitrov where we allow $P$ to come from a class of a multivariate polynomials, extending a result of Lind, Schmidt, and Verbitskiy. Our method draws from earlier work of Duke.
Codes MSC : 11J83 - Metric theory of numbers
11R06 - "PV-numbers and generalizations; other special algebraic numbers"
14G40 - Arithmetic varieties and schemes; Arakelov theory; heights
37A45 - Relations of ergodic theory with number theory and harmonic analysis
37P30
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 01/12/2020 Date de Captation : 25/11/2020 Sous Collection : Research talks Catégorie arXiv : Number Theory Domaine(s) : Théorie des Nombres Format : MP4 (.mp4) - HD Durée : 00:55:27 Audience : Chercheurs Download : https://videos.cirm-math.fr/2020-11-25_Habegger.mp4 
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Informations sur la Rencontre
Nom de la Rencontre : Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoireOrganisateurs de la Rencontre : Rivat, Joël ; Tichy, Robert Dates : 23/11/2020 - 27/11/2020 Année de la rencontre : 2020 URL de la Rencontre : https://www.chairejeanmorlet.com/2256.html
Données de citation
DOI : 10.24350/CIRM.V.19687503Citer cette vidéo: Habegger, Philipp (2020). Equidistribution of roots of unity and the Mahler measure. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19687503 URI : http://dx.doi.org/10.24350/CIRM.V.19687503 |
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Bibliographie
