2022.04.12 20:10

# [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 #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 $3$.

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