Diophantine exponents, best approximation and badly approximable numbers | Vidéo | Carmin.tv

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Diophantine exponents, best approximation and badly approximable numbers

By Nikolay Moshchevitin

Appears in collection : Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoire

We will discuss recent progress in analysis of uniform and ordinary Diophantine exponents $\hat\omega $ and $\omega$ for linear Diophantine approximation as well as some applications of the related methods. In particular, we give a new criterion for badly approximable vectors in $\mathbb{R}^{d}$ the behavior of the best approximation vectors in the sense of simultaneous approximation and in the sense of linear form. It turned out that compared to the one-dimensional case our criterion is rather unusual. We apply this criterion to the analysis of Dirichlet spectrum for simultaneous Diophantine approximation.

Information about the video

Date of recording 23/11/2020
Date of publication 01/12/2020
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19688203
Cite this video Moshchevitin, Nikolay (23/11/2020). Diophantine exponents, best approximation and badly approximable numbers. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19688203
URL https://dx.doi.org/10.24350/CIRM.V.19688203

Domain(s)

Number Theory

Bibliography

MARNAT, Antoine et MOSHCHEVITIN, Nikolay G. An optimal bound for the ratio between ordinary and uniform exponents of Diophantine approximation. Mathematika, 2020, vol. 66, no 3, p. 818-854. - https://doi.org/10.1112/mtk.12045
AKHUNZHANOV, Renat et MOSHCHEVITIN, Nikolay. On badly approximable numbers. arXiv preprint arXiv:2002.00433, 2020. - https://arxiv.org/abs/2002.00433

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