Variant of the truncated Perron formula and primes in polynomial sets-Reference-Cited by-同舟云学术

Variant of the truncated Perron formula and primes in polynomial sets

Published:2019-09-05 Issue:02 Volume:16 Page:309-323
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Ramana D. S.¹,Ramaré O.²

Affiliation:

1. HBNI/Harish-Chandra Research Institute, Jhunsi, Allahabad 211 019, India

2. CNRS/Institut de Mathématiques de Marseille, Aix Marseille Université, Centrale Marseille, Site Sud, Campus de Luminy, Case 907, 13288 Marseille Cedex 9, France

Abstract

We show under the Generalized Riemann Hypothesis that for every non-constant integer-valued polynomial [Formula: see text], for every [Formula: see text], and almost every prime [Formula: see text] in [Formula: see text], the number of primes from the interval [Formula: see text] that are values of [Formula: see text] modulo [Formula: see text] is the expected one, provided [Formula: see text] is not more than [Formula: see text]. We obtain this via a variant of the classical truncated Perron’s formula for the partial sums of the coefficients of a Dirichlet series.

Funder

CEFIPRA

EPSRC

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042120500165

Reference8 articles.

1. Sur la fonction $\zeta(s)$ de Riemann et sur des fonctions analogues

2. On the symmetry of the divisor function in almost all short intervals

3. On a conjecture of Schur.

4. Analytic Number Theory

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