The aim of this paper is to provide detailed estimates for the discrepancy of the sequences ([: } s q (n)]) ([x] denotes the fractional part of x) and results concerning the uniform distribution and the discrepancy of the sequences ([: 1 } s q 1 (n)], ..., [: d } s q d (n)]), where :, : 1 , ..., : d
On the joint distribution of digital sums
β Scribed by Jerome A. Solinas
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 606 KB
- Volume
- 33
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let Q=[Q j ] j=0 be a strictly increasing sequence of integers with Q 0 =1 and such that each Q j is a divisor of Q j+1 . The sequence Q is a numeration system in the sense that every positive integer n has a unique ``base-Q'' representation of the form n= j 0 a j (n) Q j with ``digits'' a j (n) sat
## Abstract We consider the continued fraction digits as random variables measured with respect to Lebesgue measure. The logarithmically scaled and normalised fluctuation process of the digit sums converges strongly distributional to a random variable uniformly distributed on the unit interval. For
Canonical number systems are the natural generalization of q-adic number systems to number fields. Such number systems admit a certain representation of each algebraic integer of a given number field with respect to the powers of a given base number b. The aim of this paper is to study the sum of di