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- W4297954968 abstract "This text is devoted to simultaneous approximation to $xi$ and $xi^2$ by rational numbers with the same denominator, where $xi$ is a non-quadratic real number. We focus on an exponent $beta_0(xi)$ that measures the quality of such approximations (when they are exceptionally good). We prove that $beta_0$ takes the same set of values as a combinatorial quantity that measures the abundance of palindrome prefixes in an infinite word $w$. This allows us to give a precise exposition of Roy's palindrome prefix method. The main tools we use are Davenport-Schmidt's sequence of minimal points and Roy's bracket operation." @default.
- W4297954968 created "2022-10-01" @default.
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- W4297954968 date "2005-09-22" @default.
- W4297954968 modified "2023-09-29" @default.
- W4297954968 title "Palindromic Prefixes and Diophantine Approximation" @default.
- W4297954968 doi "https://doi.org/10.48550/arxiv.math/0509508" @default.
- W4297954968 hasPublicationYear "2005" @default.
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