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We obtain new results regarding the precise average-case analysis of the main quantities that intervene in algorithms of a broad Euclidean type. We develop a general framework for the analysis of such algorithms, where the average-case complexity of an algorithm is related to the analytic behaviour in the complex plane of the set of elementary transformations determined by the algorithms. The methods rely on properties of transfer operators suitably adapted from dynamical systems theory and provide...

Dimension des courbes planes, papiers plies et suites de Rudin-Shapiro

Michel Mendès France, G. Tenenbaum (1981)

Bulletin de la Société Mathématique de France

Distribution of integer partitions with large number of summands

Hsien-Kuei Hwang (1997)

Acta Arithmetica

Distributions de Frobénius

Marc Yor (1975/1976)

Séminaire Delange-Pisot-Poitou. Théorie des nombres

Ergodic averages with deterministic weights

Fabien Durand, Dominique Schneider (2002)

Annales de l’institut Fourier

We study the convergence of the ergodic averages $\frac{1}{N} \sum_{k = 0}^{N - 1} θ (k) f \circ T^{u_{k}}$ where ${(θ (k))}_{k \in ℕ}$ is a bounded sequence and ${(u_{k})}_{k \in ℕ}$ a strictly increasing sequence of integers such that ${Sup}_{α \in ℝ} | \sum_{k = 0}^{N - 1} θ (k) \exp (2 i π α u_{k}) | = O (N^{δ})$ 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.

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A limit theorem for the Hurwitz zeta-function with algebraic irrational parameter.

A limit theorem for the Riemann zeta-function in the complex space

A limit theorem for the Riemann zeta-function near the critical line in the complex space

A $p$ -adic study of the partial sums of the harmonic series.

A probabilistic setting for prime number theory

A set of infinite measure whose ratio set does not contain a given sequence.

A short proof of a known density result.

Arithmetic progressions of length three in subsets of a random set

Convergence in Möbius number systems.

Corrigendum to the paper "Limit theorems for the Mellin transform of the square of the Riemann zeta-function. I" (Acta Arith. 122 (2006), 173-184)

Digits and continuants in euclidean algorithms. Ergodic versus tauberian theorems

Dimension des courbes planes, papiers plies et suites de Rudin-Shapiro

Distribution of integer partitions with large number of summands

Distributions de Frobénius

Ergodic averages with deterministic weights

Errata to the paper: ``Remarks on maximum and minimum exponents in factoring'

Étude d'une classe de fonctions pseudo-aléatoires

Étude probabiliste des sommes des puissances s-ièmes

Fibonacci polynomials of order k, multinomial expansions and probability.

Large deviations of sums of independent random variables

Currently displaying 1 – 20 of 54