
Date : 20220513 (Fri) 16:00

Place : 27325 (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 $3$.
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