Product of primes in arithmetic progressions-Reference-Cited by-同舟云学术

Product of primes in arithmetic progressions

Published:2019-10-23 Issue:04 Volume:16 Page:747-766
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Ramaré Olivier¹,Srivastav Priyamvad²³,Serra Oriol⁴

Affiliation:

1. CNRS/Institut de Mathématiques de Marseille, Aix Marseille Université, U.M.R. 7373, Site Sud, Campus de Luminy, Case 907, 13288 MARSEILLE Cedex 9, France

2. Institute of Mathematical Sciences, Taramani, Chennai 600113, India

3. Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India

4. Universitat Politècnica de Catalunya, C. Pau Gargallo, 14. 08028 Barcelona, Spain

Abstract

We prove that, for all [Formula: see text] and for all invertible residue classes [Formula: see text] modulo [Formula: see text], there exists a natural number [Formula: see text] that is congruent to [Formula: see text] modulo [Formula: see text] and that is the product of exactly three primes, all of which are below [Formula: see text]. The proof is further supplemented with a self-contained proof of the special case of the Kneser Theorem we use.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042120500384

Reference27 articles.

1. A Brun–Titchmarsh inequality for weighted sums over prime numbers

2. Explicit estimates of some functions over primes

3. On the residues of products of prime numbers

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