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The class number one problem for the real quadratic fields $\mathbb {Q}(\sqrt {(an)^2+4a})$

Volume 172 / 2016

András Biró, Kostadinka Lapkova Acta Arithmetica 172 (2016), 117-131 MSC: Primary 11R11; Secondary 11R29, 11R42. DOI: 10.4064/aa7957-12-2015 Published online: 3 December 2015

Abstract

We solve unconditionally the class number one problem for the $2$-parameter family of real quadratic fields ${\mathbb Q}(\sqrt{d})$ with square-free discriminant $d=(an)^2+4a$ for positive odd integers $a$ and $n$.

Authors

  • András BiróA. Rényi Institute of Mathematics
    Hungarian Academy of Sciences
    Reáltanoda u. 13-15
    1053 Budapest, Hungary
    e-mail
  • Kostadinka LapkovaA. Rényi Institute of Mathematics
    Hungarian Academy of Sciences
    Reáltanoda u. 13-15
    1053 Budapest, Hungary
    e-mail

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