Hostname: page-component-7c8c6479df-xxrs7 Total loading time: 0 Render date: 2024-03-28T23:02:01.003Z Has data issue: false hasContentIssue false

Square-free values of quadratic polynomials

Published online by Cambridge University Press:  30 April 2010

J. B. Friedlander
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada (frdlndr@math.toronto.edu)
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≤ mM, 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.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2010