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.
Domaines
Théorie des nombres [math.NT]Origine | Fichiers produits par l'(les) auteur(s) |
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