Diophantine approximation of a single irrational number
โ Scribed by Jingcheng Tong
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 193 KB
- Volume
- 35
- Category
- Article
- ISSN
- 0022-314X
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๐ SIMILAR VOLUMES
## Abstract The author considers rings of rational numbers which are integral at all the primes except, possibly, primes contained in a finite set. In such rings a Diophantine definition of โค is constructed to show that all the recursively enumerable subsets of the ring are Diophantine.
Let m, n be positive integers and let : Z n ร R be a non-negative function. Let W(m, n; ) be the set { X # R mn : " : n j=1 x ij q j " < (q), 1 i m, for infinitely many q # Z n = . The Hausdorff dimension of W(m, n; ) is obtained for arbitrary non-negative functions , with no monotonicity assumpti