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1
Content available remote

Explicit estimates on the summatory functions of the Möbius function with coprimality restrictions

100%
Ramaré O.
Acta Arithmetica
|
2014
|
tom 165
|
nr 1
1-10
EN
We prove that $|∑_{d≤x,(d,q)=1} μ(d)/d| ≤ 2.4(q/φ(q))/log(x/q)$ for every x > q ≥ 1, and similar estimates for the Liouville function. We also give better constants when x/q is large.,
2
Content available remote

From explicit estimates for primes to explicit estimates for the Möbius function

100%
Ramaré O.
Acta Arithmetica
|
2013
|
tom 157
|
nr 4
365-379
3
Content available remote

Explicit estimates for the summatory function of Λ(n)/n from the one of Λ(n)

100%
Ramaré O.
Acta Arithmetica
|
2013
|
tom 159
|
nr 2
113-122
EN
We prove that the error term $∑ _{n≤x} Λ(n)/n - logx + γ$ differs from (ψ(x)-x)/x by a well controlled function. We deduce very precise numerical results from the formula obtained.
4
Content available remote

Approximate formulae for L(1,χ)

88%
Ramaré O.
Acta Arithmetica
|
2001
|
tom 100
|
nr 3
245-266
5
Content available remote

Approximate formulae for L(1,χ), II

75%
Ramaré O.
Acta Arithmetica
|
2004
|
tom 112
|
nr 2
141-149
6
Content available remote

Almost periodicity of some error terms in prime number theory

64%
Kaczorowski J., Ramaré O.
Acta Arithmetica
|
2003
|
tom 106
|
nr 3
277-297
7
Content available remote

Discrepancy estimates for some linear generalized monomials

64%
Hofer R., Ramaré O.
Acta Arithmetica
|
2016
|
tom 173
|
nr 2
183-196
EN
We consider sequences modulo one that are generated using a generalized polynomial over the real numbers. Such polynomials may also involve the integer part operation [·] additionally to addition and multiplication. A well studied example is the (nα) sequence defined by the monomial αx. Their most basic sister, $([nα]β)_{n≥0}$, is less investigated. So far only the uniform distribution modulo one of these sequences is resolved. Completely new, however, are the discrepancy results proved in this paper. We show in particular that if the pair (α,β) of real numbers is in a certain sense badly approximable, then the discrepancy satisfies a bound of order $𝓞_{α,β,ε}(N^{-1+ε})$.
8
Content available remote

Improving on the Brun-Titchmarsh theorem

64%
Ramaré O., Schlage-Puchta J.-C.
Acta Arithmetica
|
2008
|
tom 131
|
nr 4
351-366
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