Corrigendum to my paper "On twin almost primes" and an addendum on Selberg's sieve
Corrigendum zur Arbeit „Über die reellen Nullstellen der Dirichletschen L-Reihen"
Counting monic irreducible polynomials in for which order of is odd
Hasse showed the existence and computed the Dirichlet density of the set of primes for which the order of is odd; it is . Here we mimic successfully Hasse’s method to compute the density of monic irreducibles in for which the order of is odd. But on the way, we are also led to a new and elementary proof of these densities. More observations are made, and averages are considered, in particular, an average of the ’s as varies through all rational primes.
Démonstration élémentaire du théorème des nombres premiers
Density Functions for Prime and Relatively Prime Numbers.
Density results for the 2-classgroups of imaginary quadratic fields.
Des exemples de programmation non linéaire en théorie des nombres
Des exemples de programmation non linéaire en théorie des nombres
Determining Mills' constant and a note on Honaker's problem.
Développement asymptotique de la somme des inverses d’une fonction arithmétique
La somme des puissances des inverses de , désignant le nombre de nombres premiers n’excédant pas , a fait l’objet de nombreux travaux. Nous généralisons, dans cet article, les formules asymptotiques obtenues par ces auteurs à toute une classe de fonctions arithmétiques.
Dichtentheoretische Sätze der Primzahltheorie.
Die Bestimmung der Dichtigkeit einer Menge von Primzahlen, welche zu einer gegebenen Substitutionsklasse gehören
Die Primteilerdichte von ganzzahligen Polynomen.
Die Primteilerdichte von ganzzahligen Polynomen. I.
Differences between consecutive primes
Differences between prime numbers
Discretization of prime counting functions, convexity and the Riemann hypothesis
We study tails of prime counting functions. Our approach leads to representations with a main term and an error term for the asymptotic size of each tail. It is further shown that the main term is of a specific shape and can be written discretely as a sum involving probabilities of certain events belonging to a perturbed binomial distribution. The limitations of the error term in our representation give us equivalent conditions for various forms of the Riemann hypothesis, for classical type zero-free...
Distribution des nombres premiers et fonction
Distribution of irregular prime numbers.
Distribution of primes and a weighted energy problem.