Some Metrical Theorems of Diophantine Approximation (II)
โ Scribed by Cassels, J. W. S.
- Book ID
- 120099160
- Publisher
- Oxford University Press
- Year
- 1950
- Tongue
- English
- Weight
- 125 KB
- Volume
- s1-25
- Category
- Article
- ISSN
- 0024-6107
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
We investigate rational approximations รฐr=p; q=pร or รฐr=p; q=rร to points on the curve รฐa; a t ร for almost all a > 0; where p; q; r are all primes. We immediately obtain corollaries on making p; ยฝap; ยฝa t p simultaneously prime. # 2002 Elsevier Science (USA)
Let x be a real number in [0, 1], F n be the Farey sequence of order n and \ n (x) be the distance between x and F n . The first result concerns the average rate of approximation: The second result states that any badly approximable number is better approximable by rationals than all numbers in ave