On the representation of integers by binary forms

  • C. L. StewartEmail author
  • Stanley Yao Xiao


Let F be a binary form with integer coefficients, non-zero discriminant and degree d with d at least 3. Let \(R_F(Z)\) denote the number of integers of absolute value at most Z which are represented by F. We prove that there is a positive number \(C_F\) such that \(R_F(Z)\) is asymptotic to \(C_F Z^{\frac{2}{d}}\).

Mathematics Subject Classification

Primary 11D45 Secondary 11D59 11E76 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of WaterlooWaterlooCanada
  2. 2.Department of MathematicsUniversity of Toronto, Bahen CentreTorontoCanada

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