Smooth values of shifted primes in arithmetic progressions

William D. Banks, Asma Harcharras, Igor E. Shparlinski

Type: Article

Publication Date: 2004-11-16

Citations: 3

DOI: https://doi.org/10.1307/mmj/1100623415

Abstract

We study the problem of bounding the number of primes p ≤ x in an arithmetic progression for which the largest prime factor of p − h does not exceed y.

Locations

The Michigan Mathematical Journal - View - PDF

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+	Autour des plus grands facteurs premiers d’entiers consÉcutifs voisins d’un entier criblÉ	2018	Zhiwei Wang
+ PDF Chat	Distributional properties of the largest prime factor	2005	William D. Banks Glyn Harman Igor E. Shparlinski

Works Cited by This (15)

Action	Title	Year	Authors
+	Introduction to Analytic and Probabilistic Number Theory	2015	Gérald Tenenbaum
+ PDF Chat	Smooth Orders and Cryptographic Applications	2002	Carl Pomerance Igor E. Shparlinski
+ PDF Chat	Shifted primes without large prime factors	1998	Roger C. Baker G. Harman
+	Polynomial values free of large prime factors	2002	Cécile Dartyge Gérald Tenenbaum Greg Martin
+	An Asymptotic Formula for the Number of Smooth Values of a Polynomial	2002	Greg Martin
+	On the number of positive integers ≦ x and free of prime factors > y	1986	Adolf Hildebrand
+	Entiers Sans Grand Facteur Premier En Progressions Arithmetiques	1991	Étienne Fouvry Gérald Tenenbaum
+	ON THE NORMAL NUMBER OF PRIME FACTORS OF <i>p</i>-1 AND SOME RELATED PROBLEMS CONCERNING EULER'S ø-FUNCTION	1935	P. Erdős
+	Integers, without large prime factors, in arithmetic progressions. II	1993	Andrew Granville
+	Répartition Statistique Des Entiers Sans Grand Facteur Premier Dans Les Progressions Arithmétiques	1996	Étienne Fouvry Gérald Tenenbaum