Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-22T15:34:15.897Z Has data issue: false hasContentIssue false
  • English
  • Français

Square-free values of quadratic polynomials

Part of: Multiplicative number theory

Published online by Cambridge University Press:  30 April 2010

J. B. Friedlander  and
H. Iwaniec
J. B. Friedlander
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada ([email protected])
H. Iwaniec
Affiliation:
Department of Mathematics, Rutgers University, Piscataway, NJ 08903, USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider the quadratic polynomial m2 + D and study the asymptotic formula for the number of integers m, 1≤ m ≤ M, for which the values of the polynomial are square-free. We are interested in particular in the question of how small we can take m in relation to D and still have the asymptotic hold.

Keywords

quadratic polynomialsquare-free numbers

MSC classification

Secondary: 11N32: Primes represented by polynomials; other multiplicative structure of polynomial values 11N35: Sieves
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 2 , June 2010 , pp. 385 - 392
Copyright
Copyright © Edinburgh Mathematical Society 2010