Simultaneous Representation of Integers by a Pair of Ternary Quadratic Forms—With an Application to Index Form Equations in Quartic Number Fields

@inproceedings{Gal1996SimultaneousRO,
  title={Simultaneous Representation of Integers by a Pair of Ternary Quadratic Forms—With an Application to Index Form Equations in Quartic Number Fields},
  author={Istv{\'a}n Ga{\'a}l and Attila Pethǒ and Michael E. Pohst},
  year={1996}
}
Abstract Let Q 1 ,  Q 2 ∈ Z [ X ,  Y ,  Z ] be two ternary quadratic forms and u 1 ,  u 2 ∈ Z . In this paper we consider the problem of solving the system of equations[formula]According to Mordell [12] the coprime solutions of[formula]can be presented by finitely many expressions of the form x = f x ( p ,  q ), y = f y ( p ,  q ), z = f z ( p ,  q ), where f x ,  f y ,  f z ∈ Z [ P ,  Q ] are binary quadratic forms and p ,  q are coprime integers. Substituting these expressions into one of the… CONTINUE READING