Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5778904 | Indagationes Mathematicae | 2017 | 18 Pages |
Abstract
We establish new inequalities involving classical exponents of Diophantine approximation. This allows for improving on the work of H. Davenport, W.M. Schmidt and M. Laurent concerning the maximum value of the exponent λÌn(ζ) among all real transcendental ζ. In particular we refine the estimation λÌn(ζ)â¤ân/2ââ1 due to M. Laurent by λÌn(ζ)â¤wÌân/2â(ζ)â1 for all nâ¥1, and for even n we replace the bound 2/n for λÌn(ζ) first found by Davenport and Schmidt by roughly 2nâ4n3, which provides the currently best known bound when nâ¥6.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Johannes Schleischitz,