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On the Littlewood Conjecture in Simultaneous Diophantine Approximation
Author(s) -
Adamczewski Boris,
Bugeaud Yann
Publication year - 2006
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610706022617
Subject(s) - quotient , conjecture , diophantine approximation , mathematics , bounded function , lonely runner conjecture , diophantine equation , pure mathematics , beta (programming language) , alpha (finance) , discrete mathematics , combinatorics , collatz conjecture , mathematical analysis , computer science , programming language , construct validity , statistics , psychometrics
For any given real number α with bounded partial quotients, we construct explicitly continuum many real numbers β with bounded partial quotients for which the pair (α, β) satisfies a strong form of the Littlewood conjecture. Our proof is elementary and rests on the basic theory of continued fractions.