$\alpha$-additive functions and uniform distribution modulo one

On uniform distribution modulo one

We introduce an elementary argument to the theory of distribution of sequences modulo one.

Distribution 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...

Uniform Distribution modulo 1 and the Universality of Zeta-functions of Certain Cusp Forms

An universality theorem on the approximation of analytic functions by shifts ζ(s+iτ, F ) of zeta-functions of normalized Hecke-eigen forms F , where τ takes values from the set {kαh : k = 0, 1, 2, . . . } with fixed 0 < α < 1 and h > 0, is obtained.

Uniform 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.

q-ADDITIVE FUNCTIONS AND WELL DISTRIBUTION