A Note on the Field Isomorphism Problem of X3+sX+s and Related Cubic Thue Equations (Japan-Korea joint seminar on number theory and related topics 2008) A Note on the Field Isomorphism Problem of X3+sX+s and Related Cubic Thue Equations

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Author(s)

    • MIYAKE Katsuya
    • Department of Mathematics, School of Fundamental Science and Engineering, Waseda University

Abstract

We study the field isomorphism problem of cubic generic polynomial <I>X</I><SUP>3</SUP>+<I>sX</I>+<I>s</I> over the field of rational numbers with the specialization of the parameter <I>s</I> to nonzero rational integers <I>m</I> via primitive solutions to the family of cubic Thue equations <I>x</I><SUP>3</SUP>−2<I>mx</I><SUP>2</SUP><I>y</I>−9<I>mxy</I><SUP>2</SUP>−<I>m</I>(2<I>m</I>+27)<I>y</I><SUP>3</SUP>=λ where λ<SUP>2</SUP> is a divisor of <I>m</I><SUP>3</SUP>(4<I>m</I>+27)<SUP>5</SUP>.

Journal

  • Interdisciplinary Information Sciences

    Interdisciplinary Information Sciences 16(1), 45-54, 2010

    Graduate School of Information Sciences, Tohoku University

Codes

  • NII Article ID (NAID)
    110009794873
  • NII NACSIS-CAT ID (NCID)
    AA11032627
  • Text Lang
    ENG
  • Article Type
    departmental bulletin paper
  • ISSN
    1340-9050
  • Data Source
    NII-ELS  IR  J-STAGE 
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