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
SN - 1073-2780
VL - 15
SP - 1133
EP - 1147
JO - Mathematical Research Letters
JF - Mathematical Research Letters
IS - 5-6
ER -