qsms.math.snu.ac.kr - [SNU Number Theory Seminar 2022-05-13] A singular function containing all Lagrange numbers less than three

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일정시작	2022-05-13
배경색상	#FF5733

일정시작

2022-05-13

배경색상

#FF5733

Date : 2022-05-13 (Fri) 16:00
Place : 27-325 (SNU)
Speaker : DoYong Kwon (Chonnam National University)
Title : A singular function containing all Lagrange numbers less than three
Abstract : Given a real number $\alpha$, the Lagrange number of $\alpha$ is the supremum of all real numbers $L>0$ for which the inequality $|\alpha -p/q|<(L q^2)^{-1}$ holds for infinitely many rational numbers $p/q$. If Lagrange numbers are less than $3$, then they characterize some badly approximable real numbers in the context of Diophantine approximations. Moreover, they can be arranged as a set $\{l_{p/q}: p/q\in \mathbb{Q}\cap [0,1] \}$ using the Farey index. The present talk considers a singular function devised from Sturmian words. After investigating its regularity and singularity, we demonstrate that this function contains all information on Lagrange numbers less than $3$.
Website: https://sites.google.com/view/snunt/seminars

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QSMS Mailing List Registration

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2021.09.09

37513

[QSMS Representation theory seminar-20240716] Highest weight categories and quasi-hereditary algebras

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