Uniform distribution modulo one on subsequences
نویسندگان
چکیده
منابع مشابه
On uniform distribution modulo one
We introduce an elementary argument to the theory of distribution of sequences modulo one.
متن کاملSubsequences of automatic sequences and uniform distribution
Automatic sequences and their number theoretic properties have been intensively studied during the last 20 or 30 years. Since automatic sequences are quite regular (they just have linear subword complexity) they cannot be used as quasi-random sequences. However, the situation changes drastically when one uses proper subsequences, for example the subsequence along primes or squares. It is conjec...
متن کاملUniform Distribution modulo One of Some Sequences concerning the Euler Function
In this paper, we follow the recent method in the theory of uniform distribution, developed by J.-M. Deshouillers and H. Iwaniec, to prove uniform distribution modulo one of various sequences involving the Euler function, together with some generalizations.
متن کاملDistribution modulo One and Ratner’s Theorem
Contents 1. Introduction 1 2. Randomness of point sequences mod 1 2 2.1. Distribution of gaps 4 2.2. Independent random variables 6 3. mα mod one 7 3.1. Geometry of Γ\G 9 3.2. Dynamics on Γ\G 10 3.3. Mixing and uniform distribution 12 4. √ mα mod one 14 4.1. The case α = 1 15 4.2. Some heuristics in the case α = √ 2 16 5. Ratner's theorem 19 5.1. Limit distributions of translates 19 5.2. Equidi...
متن کاملThe distribution of α p modulo one 269
We prove that, for any irrational number α, there are infinitely many primes p such that ‖αp‖ < p−1/3+ . Here ‖y‖ denotes the distance from y to the nearest integer. The proof uses Harman’s sieve method with arithmetical information coming from bounds for averages of Kloosterman sums.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1999
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-99-04877-7