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Title of Journal: Mh Math

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Abbravation: Monatshefte für Mathematik

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Springer-Verlag

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10.1016/0039-128x(76)90002-7

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1436-5081

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Palindromic Prefixes and Diophantine Approximation

Authors: Stéphane Fischler
Publish Date: 2006/10/16
Volume: 151, Issue: 1, Pages: 11-37
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Abstract

This article is devoted to simultaneous approximation to ξ and ξ2 by rational numbers with the same denominator where ξ is an irrational nonquadratic real number We focus on an exponent β0ξ that measures the regularity of the sequence of all exceptionally precise such approximants We prove that β0ξ takes the same set of values as a combinatorial quantity that measures the abundance of palindromic prefixes in an infinite word w This allows us to give a precise exposition of Roy’s palindromic prefix method The main tools we use are DavenportSchmidt’s sequence of minimal points and Roy’s bracket operation

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Other Papers In This Journal:
  1. A central limit theorem for integer partitions
  2. Fully commutative elements in finite and affine Coxeter groups
  3. On semi-rational finite simple groups
  4. Integer-valued polynomials over matrices and divided differences
  5. On mean values of multiplicative functions on the symmetric group
  6. Simple exceptional groups of Lie type are determined by their character degrees
  7. Löwner chains with complex leading coefficient
  8. On a functional equation related to derivations in prime rings
  9. Ricci solitons and odd-dimensional spheres
  10. Regularity properties of distributions through sequences of functions
  11. An explicit growth condition for middle-degree cuspidal cohomology of arithmetically defined quaternionic hyperbolic n -manifolds
  12. Operations with monotone operators and the monotonicity of the resulting operators
  13. Normal families of meromorphic functions and shared values
  14. Some New Results on the Chu Duality of Discrete Groups
  15. Cauchy integral and singular integral operator over closed Jordan curves
  16. The zero-free region of the derivative of Selberg zeta functions
  17. A note on Engel words of finite groups
  18. Equivalence of plurisubharmonic singularities and Siu-type metrics
  19. Effective uniqueness of Parry measure and exceptional sets in ergodic theory
  20. On matrix valued square integrable positive definite functions
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