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Acta Arithmetica

Almost periodic sequences and functions with given values

Archivum Mathematicum

We present a method for constructing almost periodic sequences and functions with values in a metric space. Applying this method, we find almost periodic sequences and functions with prescribed values. Especially, for any totally bounded countable set $X$ in a metric space, it is proved the existence of an almost periodic sequence ${\left\{{\psi }_{k}\right\}}_{k\in ℤ}$ such that $\left\{{\psi }_{k};\phantom{\rule{0.166667em}{0ex}}k\in ℤ\right\}=X$ and ${\psi }_{k}={\psi }_{k+lq\left(k\right)}$, $l\in ℤ$ for all $k$ and some $q\left(k\right)\in ℕ$ which depends on $k$.

Acta Arithmetica

Acta Arithmetica

Dirichlet series induced by the Riemann zeta-function

Studia Mathematica

The Riemann zeta-function ζ(s) extends to an outer function in ergodic Hardy spaces on ${}^{\omega }$, the infinite-dimensional torus indexed by primes p. This enables us to investigate collectively certain properties of Dirichlet series of the form $\left({a}_{p},s\right)={\prod }_{p}{\left(1-{a}_{p}{p}^{-s}\right)}^{-1}$ for ${a}_{p}$ in ${}^{\omega }$. Among other things, using the Haar measure on ${}^{\omega }$ for measuring the asymptotic behavior of ζ(s) in the critical strip, we shall prove, in a weak sense, the mean-value theorem for ζ(s), equivalent to the Lindelöf hypothesis.

Distribution of values of a real function: Means, moments, and symmetry.

Manuscripta mathematica

Integers

Acta Arithmetica

Le théorème ergodique le long d’une suite $q$-multiplicative

Compositio Mathematica

Mesures spectrales associées à certaines suites arithmétiques

Bulletin de la Société Mathématique de France

Od funkcí periodických ke skoroperiodickým

Pokroky matematiky, fyziky a astronomie

Semigroup forum

Acta Arithmetica

Acta Arithmetica

Ramanujan sums and almost periodic functions

Studia Mathematica

The multiplicative group of rationals generated by the shifted primes, I.

Journal für die reine und angewandte Mathematik

Une classe d'ensembles d'unicité des séries trigonométriques

Séminaire Delange-Pisot-Poitou. Théorie des nombres

Universal Spectra and Tijdeman's Conjecture on Factorization of Cyclic Groups.

The journal of Fourier analysis and applications [[Elektronische Ressource]]

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