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Number of solutions of cubic Thue inequalities with positive discriminant

Volume 171 / 2015

N. Saradha, Divyum Sharma Acta Arithmetica 171 (2015), 81-95 MSC: Primary 11D45, 11D75; Secondary 11E76, 11D25. DOI: 10.4064/aa171-1-6

Abstract

Let $F(X,Y)$ be an irreducible binary cubic form with integer coefficients and positive discriminant $D$. Let $k$ be a positive integer satisfying \[ k<\frac {(3D)^{1/4}}{2\pi }. \] We give improved upper bounds for the number of primitive solutions of the Thue inequality \[ |F(X,Y)|\leq k. \]

Authors

  • N. SaradhaSchool of Mathematics
    Tata Institute of Fundamental Research
    Homi Bhabha Road
    Mumbai 400 005, India
    e-mail
  • Divyum SharmaSchool of Mathematics
    Tata Institute of Fundamental Research
    Homi Bhabha Road
    Mumbai 400 005, India
    e-mail

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