Friable values of binary forms

  • Antal Balog

    Hungarian Academy, Budapest, Hungary
  • Valentin Blomer

    Georg-August-Universität Göttingen, Germany
  • Cécile Dartyge

    Université Henri Poincaré, Vandoeuvre lès Nancy, France
  • Gérald Tenenbaum

    Université de Lorraine, Vandoeuvre-lès-Nancy, France


Let be an integral binary form of degree , and let

where as usual denotes the largest prime factor of . It is proved that for in general, and if . Better results are obtained if is reducible.

Cite this article

Antal Balog, Valentin Blomer, Cécile Dartyge, Gérald Tenenbaum, Friable values of binary forms. Comment. Math. Helv. 87 (2012), no. 3, pp. 639–667

DOI 10.4171/CMH/264