Products in residue classes

John B. Friedlander; Pär Kurlberg; Igor E. Shparlinski

Products in residue classes

John B. Friedlander, Pär Kurlberg, Igor E. Shparlinski

Department of Computing

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

We consider a problem of P. Erdos, A. M. Odlyzko and A. Sárkozy about the representation of residue classes modulo m by products of two not too large primes. While it seems that even the Extended Riemann Hypothesis is not powerful enough to achieve the expected results, here we obtain some unconditional results "on average" over moduli m and residue classes modulo m and somewhat stronger results when the average is restricted to prime moduli m = p. We also consider the analogous question wherein the primes are replaced by easier sequences so, quite naturally, we obtain much stronger results.

Original language	English
Pages (from-to)	1133-1147
Number of pages	15
Journal	Mathematical Research Letters
Volume	15
Issue number	5-6
Publication status	Published - Sep 2008

Access to Document

Link to publication in Scopus

Fingerprint Dive into the research topics of 'Products in residue classes'. Together they form a unique fingerprint.

Cite this

@article{8739930a74c54b66a5530d170e5b2bd2,

title = "Products in residue classes",

abstract = "We consider a problem of P. Erdos, A. M. Odlyzko and A. S{\'a}rkozy about the representation of residue classes modulo m by products of two not too large primes. While it seems that even the Extended Riemann Hypothesis is not powerful enough to achieve the expected results, here we obtain some unconditional results {"}on average{"} over moduli m and residue classes modulo m and somewhat stronger results when the average is restricted to prime moduli m = p. We also consider the analogous question wherein the primes are replaced by easier sequences so, quite naturally, we obtain much stronger results.",

author = "Friedlander, {John B.} and P{\"a}r Kurlberg and Shparlinski, {Igor E.}",

year = "2008",

month = sep,

language = "English",

volume = "15",

pages = "1133--1147",

journal = "Mathematical Research Letters",

issn = "1073-2780",

publisher = "International Press of Boston, Inc.",

number = "5-6",

}

TY - JOUR

T1 - Products in residue classes

AU - Friedlander, John B.

AU - Kurlberg, Pär

AU - Shparlinski, Igor E.

PY - 2008/9

Y1 - 2008/9

N2 - We consider a problem of P. Erdos, A. M. Odlyzko and A. Sárkozy about the representation of residue classes modulo m by products of two not too large primes. While it seems that even the Extended Riemann Hypothesis is not powerful enough to achieve the expected results, here we obtain some unconditional results "on average" over moduli m and residue classes modulo m and somewhat stronger results when the average is restricted to prime moduli m = p. We also consider the analogous question wherein the primes are replaced by easier sequences so, quite naturally, we obtain much stronger results.

AB - We consider a problem of P. Erdos, A. M. Odlyzko and A. Sárkozy about the representation of residue classes modulo m by products of two not too large primes. While it seems that even the Extended Riemann Hypothesis is not powerful enough to achieve the expected results, here we obtain some unconditional results "on average" over moduli m and residue classes modulo m and somewhat stronger results when the average is restricted to prime moduli m = p. We also consider the analogous question wherein the primes are replaced by easier sequences so, quite naturally, we obtain much stronger results.

UR - http://www.scopus.com/inward/record.url?scp=59349120796&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:59349120796

VL - 15

SP - 1133

EP - 1147

JO - Mathematical Research Letters

JF - Mathematical Research Letters

SN - 1073-2780

IS - 5-6

ER -