Congruent numbers over real number fields

Volume 128 / 2012

Tomasz Jędrzejak Colloquium Mathematicum 128 (2012), 179-186 MSC: Primary 11G05; Secondary 14H52. DOI: 10.4064/cm128-2-3

Abstract

It is classical that a natural number $n$ is congruent iff the rank of $\mathbb{Q}$-points on $E_{n}:y^{2}=x^{3}-n^{2}x$ is positive. In this paper, following Tada (2001), we consider generalised congruent numbers. We extend the above classical criterion to several infinite families of real number fields.

Authors

  • Tomasz JędrzejakInstitute of Mathematics
    University of Szczecin
    Wielkopolska 15
    70-451 Szczecin, Poland
    e-mail

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