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Equidistribution of roots of unity and the Mahler measure
Virtualconference
Authors : Habegger, Philipp (Author of the conference)
CIRM (Publisher )
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 (Publisher )
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Abstract :
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.
MSC Codes : 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 01/12/2020 Conference Date : 25/11/2020 Subseries : Research talks arXiv category : Number Theory Mathematical Area(s) : Number Theory Format : MP4 (.mp4) - HD Video Time : 00:55:27 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2020-11-25_Habegger.mp4 
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Information on the Event
Event Title : Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoireEvent Organizers : Rivat, Joël ; Tichy, Robert Dates : 23/11/2020 - 27/11/2020 Event Year : 2020 Event URL : https://www.chairejeanmorlet.com/2256.html
Citation Data
DOI : 10.24350/CIRM.V.19687503Cite this video as: 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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