Almost all short intervals containing prime numbers
Almost-primes represented by quadratic polynomials
An additive problem with primes and almost-primes
An average form of Artin's conjecture
Arithmetic progressions of prime-almost-prime twins
Arithmetical semigroups II: sieving by large and small prime elements. Sets of multiples.
Autour de la conjecture de Sato-Tate pour les sommes de Kloosterman I.
Averages of twisted elliptic L-functions
Bombieri-Vinogradov type theorems for sparse sets of moduli
Chen's theorem in short intervals
Chen's theorem in totally real algebraic number fields
Composite positive integers whose sum of prime factors is prime
In this note, we show that the counting function of the number of composite positive integers such that is a prime is of order of magnitude at least and at most .
Concentration function of additive functions on shifted twin primes
Concentration function of additive functions on shifted twin primes
0. Introduction. The content of this paper is part of the author's Ph.D. thesis. The two new theorems in this paper provide upper bounds on the concentration function of additive functions evaluated on shifted γ-twin prime, where γ is any positive even integers. Both results are generalizations of theorems due to I. Z. Ruzsa, N. M. Timofeev, and P. D. T. A. Elliott.
Consecutive primes in tuples
In a stunning new advance towards the Prime k-Tuple Conjecture, Maynard and Tao have shown that if k is sufficiently large in terms of m, then for an admissible k-tuple of linear forms in ℤ[x], the set contains at least m primes for infinitely many n ∈ ℕ. In this note, we deduce that contains at least m consecutive primes for infinitely many n ∈ ℕ. We answer an old question of Erdős and Turán by producing strings of m + 1 consecutive primes whose successive gaps form an increasing (resp....
Corrigendum to the paper "Additive problems with prime numbers of special type" (Acta Arith. 96 (2000), 53-88)
Crible asymptotique et sommes de Kloosterman
On montre à l’aide de méthodes de crible, de méthodes issues de la théorie des formes automorphes et de géométrie algébrique ainsi qu’à l’aide de la loi de Sato-Tate verticale que le signe des sommes de Kloosterman change une infinité de fois pour parcourant les entiers sans facteur carré ayant au plus facteurs premiers. Ceci améliore un résultat précédent de Fouvry et Michel qui avaient obtenu à la place de .
Crible et 3-rang des corps quadratiques
Considérons le cardinal de l’ensemble des racines cubiques de l’unité dans le groupe des classes de , où est un discriminant fondamental. Un résultat de Davenport et Heilbronn calcule la valeur moyenne de ces nombres quand varie. On obtient ici géométriquement une borne explicite pour le reste, avec la possibilité supplémentaire de restreindre les à des progressions arithmétiques. Des techniques de crible permettent alors d’évaluer la 3-partie des , où est pseudo-premier d’ordre . On...
Crible étrange et sommes de Kloosterman
Cubic norms represented by quadratic sequences