From explicit estimates for primes to explicit estimates for the Möbius function
Explicit estimates on the summatory functions of the Möbius function with coprimality restrictions
We prove that for every x > q ≥ 1, and similar estimates for the Liouville function. We also give better constants when x/q is large.,
Explicit estimates for the summatory function of Λ(n)/n from the one of Λ(n)
We prove that the error term differs from (ψ(x)-x)/x by a well controlled function. We deduce very precise numerical results from the formula obtained.
Approximate formulae for L(1,χ), II
Approximate formulae for L(1,χ)
On šnirel'man's constant
A purely analytical lower bound for
We give a simple proof of when is an odd primitiv quadratic Dirichlet character of conductor . In particular we do not use the Dirichlet class-number formula.
Eigenvalues in the large sieve inequality, II
We explore numerically the eigenvalues of the hermitian form when . We improve on the existing upper bound, and produce a (conjectural) plot of the asymptotic distribution of its eigenvalues by exploiting fairly extensive computations. The main outcome is that this asymptotic density most probably exists but is not continuous with respect to the Lebesgue measure.
Nombres de racines d’un polynôme entier modulo
Nous montrons que l’ensemble des racines modulo une puissance d’un nombre premier d’un polynôme à coefficients entiers de degré est une union d’au plus progressions arithmétiques de modules assez grands. Nous en déduisons une majoration du nombre de ses racines dans un intervalle réel court.
Discrepancy estimates for some linear generalized monomials
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, , 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...
Almost periodicity of some error terms in prime number theory
Additive properties of dense subsets of sifted sequences
We examine additive properties of dense subsets of sifted sequences, and in particular prove under very general assumptions that such a sequence is an additive asymptotic basis whose order is very well controlled.
Improving on the Brun-Titchmarsh theorem
Page 1