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A notion of diaphony based on p-adic arithmetic

Peter Hellekalek (2010)

Acta Arithmetica

Almost periodic sequences and functions with given values

Michal Veselý (2011)

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 ${ψ_{k}}_{k \in ℤ}$ such that ${ψ_{k}; k \in ℤ} = X$ and $ψ_{k} = ψ_{k + l q (k)}$ , $l \in ℤ$ for all $k$ and some $q (k) \in ℕ$ which depends on $k$ .

Almost periodicity of some error terms in prime number theory

Jerzy Kaczorowski, Olivier Ramaré (2003)

Acta Arithmetica

Application of the circle method on multidimensional limit-periodic functions

Eugen Keil (2011)

Acta Arithmetica

Dirichlet series induced by the Riemann zeta-function

Jun-ichi Tanaka (2008)

Studia Mathematica

The Riemann zeta-function ζ(s) extends to an outer function in ergodic Hardy spaces on $^{ω}$ , the infinite-dimensional torus indexed by primes p. This enables us to investigate collectively certain properties of Dirichlet series of the form $(a_{p}, s) = \prod_{p} {(1 - a_{p} p^{- s})}^{- 1}$ for $a_{p}$ in $^{ω}$ . Among other things, using the Haar measure on $^{ω}$ 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.