The arithmetic of power series - Lecture 1 | Vidéo | Carmin.tv

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The arithmetic of power series - Lecture 1

By Yunqing Tang

Appears in collection : Diophantine approximation and transcendence 2025 / Approximation diophantienne et transcendance 2025

We will first briefly discuss our approach to prove irrationality of certain periods. Our method uses rational approximations from the literature and we develop a new framework to make use of these approximations. The key ingredient is an arithmetic holonomy theorem built upon earlier work by André, Bost, Charles (and others) on arithmetic algebraization theorems via Arakelov theory. We will then discuss our recent result on irrationality measures. This is joint work with Frank Calegari and Vesselin Dimitrov.

Information about the video

Date of recording 10/11/2025
Date of publication 26/11/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20403303
Cite this video Tang, Yunqing (10/11/2025). The arithmetic of power series - Lecture 1. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20403303
URL https://dx.doi.org/10.24350/CIRM.V.20403303

Domain(s)

Number Theory

Bibliography

CALEGARI, Frank, DIMITROV, Vesselin, et TANG, Yunqing. The linear independence of $1 $, $\zeta (2) $, and $ L (2,\chi_ {-3}) $. arXiv preprint arXiv:2408.15403, 2024. - https://doi.org/10.48550/arXiv.2408.15403
CALEGARI, Frank, DIMITROV, Vesselin, et TANG, Yunqing. Arithmetic holonomy bounds and effective Diophantine approximation. arXiv preprint arXiv:2510.04156, 2025. - https://doi.org/10.48550/arXiv.2510.04156

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