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Ergodic averages with deterministic weights

Fabien Durand, Dominique Schneider (2002)

Annales de l’institut Fourier

We study the convergence of the ergodic averages 1 N ∑ k = 0 N - 1 θ ( k ) f ∘ T u k where ( θ ( k ) ) k ∈ ℕ is a bounded sequence and ( u k ) k ∈ ℕ a strictly increasing sequence of integers such that Sup α ∈ ℝ | ∑ k = 0 N - 1 θ ( k ) exp ( 2 i π α u k ) | = O ( N δ ) for some δ < 1 . Moreover we give explicit such sequences θ and u and we investigate in particular the case where θ is a q -multiplicative sequence.

Ergodic Universality Theorems for the Riemann Zeta-Function and other L -Functions

Jörn Steuding (2013)

Journal de Théorie des Nombres de Bordeaux

We prove a new type of universality theorem for the Riemann zeta-function and other L -functions (which are universal in the sense of Voronin’s theorem). In contrast to previous universality theorems for the zeta-function or its various generalizations, here the approximating shifts are taken from the orbit of an ergodic transformation on the real line.

Ergodicity of ℤ² extensions of irrational rotations

Yuqing Zhang (2011)

Studia Mathematica

Let = [0,1) be the additive group of real numbers modulo 1, α ∈ be an irrational number and t ∈ . We study ergodicity of skew product extensions T : × ℤ² → × ℤ², T ( x , s ₁ , s ₂ ) = ( x + α , s ₁ + 2 χ [ 0 , 1 / 2 ) ( x ) - 1 , s ₂ + 2 χ [ 0 , 1 / 2 ) ( x + t ) - 1 ) .

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