@article {IOPORT.05817695,
    author       = {Alvanos, Paraskevas and Poulakis, Dimitrios},
    title        = {Solving genus zero Diophantine equations over number fields.},
    year         = {2011},
    journal      = {Journal of Symbolic Computation},
    volume       = {46},
    number       = {1},
    issn         = {0747-7171},
    pages        = {54-69},
    publisher    = {Elsevier Science (Academic Press), London},
    doi          = {10.1016/j.jsc.2010.09.002},
    abstract     = {Let $K$ be an algebraic number field and $F(X,Y)$ an absolutely irreducible polynomial with coefficients in $K$ such that the curve defined by the equation $F(X,Y)=0$ is rational. Continuing the works of {\it D. Poulakis} and {\it E. Voskos} [J. Symb. Comput. 30, No. 5, 573---582 (2000; Zbl 0985.11051), J. Symb. Comput. 33, No. 4, 479--491 (2002; Zbl 0998.11014)] the authors of the present paper give an algorithm to determine all solutions of $F(X,Y)=0$ in algebraic integers of $K$. The paper is illustrated by interesting examples. The algebraic number theory procedures necessary for these calculations are available in the well known packages.},
    reviewer     = {Istv\'an Ga\'al (Debrecen)},
    identifier   = {05817695},
}