Extra Form
Lecturer 김동한
Dept. 동국대
date Oct 27, 2016

We introduce and study a new complexity function in combinatorics on words, which takes into account the smallest return time of a factor of an infinite word. We characterize the eventually periodic words and the Sturmian words by means of this function. Then, we establish a new result on repetitions in Sturmian words and show that it is best possible. We deduce a lower bound for the irrationality exponent of real numbers whose sequence of b-ary digits is a Sturmian sequence over {0,1,…,b-1} and we prove that this lower bound is best possible. If the irrationality exponent of \xi is equal to 2 or slightly greater than 2, then the b-ary expansion of \xi cannot be `too simple', in a suitable sense. Our result applies, among other classical numbers, to badly approximable numbers, non-zero rational powers of e, and log(1+1/a), provided that the integer a is sufficiently large. It establishes an unexpected connection between the irrationality exponent of a real number and its b-ary expansion.

List of Articles
Category Subject Dept. Lecturer
Math Colloquia Noise-induced phenomena in stochastic heat equations file 포항공대 김건우
Math Colloquia Non-commutative Lp-spaces and analysis on quantum spaces file 서울대학교 이훈희
Math Colloquia Noncommutative Geometry. Quantum Space-Time and Diffeomorphism Invariant Geometry file 서울대학교 Raphael Ponge
Math Colloquia Noncommutative Surfaces file 서강대학교 Jens Hoppe
Math Colloquia Nonlocal generators of jump type Markov processes file University of Bielefeld Walter Hoh
Math Colloquia Normal form reduction for unconditional well-posedness of canonical dispersive equations file KAIST 권순식
Math Colloquia Number theoretic results in a family file Univ. of Toronto / KIAS Kim, Henry
Math Colloquia On circle diffeomorphism groups file 고등과학원 김상현
Math Colloquia On function field and smooth specialization of a hypersurface in the projective space file KAIST 이용남
Math Colloquia On Ingram’s Conjecture file University of Zagrab Sonja Stimac
Math Colloquia On some nonlinear elliptic problems file Paul Sabatier University, Toulouse Yuri Egorov
Math Colloquia On the distributions of partition ranks and cranks file 서울과학기술대학교 김병찬
Math Colloquia On the resolution of the Gibbs phenomenon file SUNY Buffalo 정재훈
Math Colloquia On the Schauder theory for elliptic PDEs file 연세대학교 김세익
Math Colloquia One and Two dimensional Coulomb Systems file 카이스트 폴정
Math Colloquia Partial differential equations with applications to biology file POSTECH 황형주
Math Colloquia Periodic orbits in symplectic geometry file 서울대 강정수
Math Colloquia Q-curvature in conformal geometry file 서강대 Pak Tung Ho
Math Colloquia Quantitative residual non-vanishing of special values of various L-functions file UNIST 선해상
Math Colloquia Quantum Dynamics in the Mean-Field and Semiclassical Regime file Ecole Polytechnique Francoise Golse
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