Variant of the truncated Perron formula and primes in polynomial sets - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue International Journal of Number Theory Année : 2020

Variant of the truncated Perron formula and primes in polynomial sets

Résumé

We show under the Generalised Riemann Hypothesis that for every non-constant integer valued polynomial $f$ , for every $\delta > 0$, and almost every prime $q$ in $[Q, 2Q]$, the number of primes from the interval $[x, x + x^{1/2 +\delta} ]$ that are values of $f$ modulo $q$ is the expected one, provided $Q$ is not more than $x^{2/3 −\varepsilon}$. We obtain this via a variant of the classical truncated Perron's formula for the partial sums of the coefficients of a Dirichlet series.
Fichier principal
Vignette du fichier
Perron4.pdf (339.29 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02585974 , version 1 (15-05-2020)

Identifiants

Citer

D. S Ramana, Olivier Ramaré. Variant of the truncated Perron formula and primes in polynomial sets. International Journal of Number Theory, 2020, 16 (02), pp.309-323. ⟨10.1142/S1793042120500165⟩. ⟨hal-02585974⟩
47 Consultations
127 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More