On a Conjecture in Diophantine Approximations, IV
โ Scribed by Y.G. Chen
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 250 KB
- Volume
- 43
- Category
- Article
- ISSN
- 0022-314X
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)
Beginning with an improvement to Dirichlet's Theorem on simultaneous approximation, in this paper we introduce an alogrithm, in sympathy with the classical continued fraction algorithm, to generate the sequence of best approximates to the system max[&: 0 n&, &: 1 n&, ..., &: L n&] in the case when :
B. deMathan (1970, Bull. Soc. Math. France Supl. Mem. 21) proved that Khintchine's Theorem has an analogue in the field of formal Laurent series. First, we show that in case of only one inequality this result can also be obtained by continued fraction theory. Then, we are interested in the number o