Integer parts of powers of rational numbers
✍ Scribed by Artūras Dubickas; Aivaras Novikas
- Publisher
- Springer-Verlag
- Year
- 2005
- Tongue
- French
- Weight
- 194 KB
- Volume
- 251
- Category
- Article
- ISSN
- 0025-5874
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract Let__p__ > __q__ > 1 be two coprime integers. In this paper, we prove several results about subsets of the interval [0, 1) which does or does not contain all the fractional parts {__ξ__ (__p__ /__q__)^__n__^ }, __n__ = 0, 1, 2, …, for certain non‐zero real number __ξ__. We show, for ins
## 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 ℤ is constructed to show that all the recursively enumerable subsets of the ring are Diophantine.