On the Asymptotic Uniform Distribution of Sums Reduced mod 1
โ Scribed by Peter Schatte
- Publisher
- John Wiley and Sons
- Year
- 1984
- Tongue
- English
- Weight
- 310 KB
- Volume
- 115
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
In this paper we seak to study the discrepancy and consequently the uniform distribution mod 1 of two types of sequences. For this purpose we denote by [ ] the integer part function. For real c with 1<c< 3 2 take (![n c ] : n=1, 2, 3, ...); here the real ! is badly approximable in the sense of \*-ad
Proof. If the Xi are replaced by -Xi, the hn(r) do not be changed. Therefore we can assume a>O. Let H,(z) be the distribution function of the random
Proof. If the Xi are replaced by -Xi, the hn(r) do not be changed. Therefore we can assume a>O. Let H,(z) be the distribution function of the random
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
A set A [1, ..., N] is of the type B 2 if all sums a+b, with a b, a, b # A, are distinct. It is well known that the largest such set is of size asymptotic to N 1ร2 . For a B 2 set A of this size we show that, under mild assumptions on the size of the modulus m and on the difference N 1ร2 &| A | (the