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Class Number Problems and Lang Conjectures

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Part of the Progress in Mathematics book series (PM,volume 321)

Abstract

Given a square-free integer d we introduce an affine hypersurface whose integer points are in one-to-one correspondence with ideal classes of the quadratic number field \(Q(\sqrt{\delta})\). Using this we relate class number problems of Gauss to Lang conjectures.

Keywords

  • Subgroups of the modular group
  • binary quadratic forms
  • class number problems
  • çark hypersurfaces
  • rational points on hypersurfaces
  • complex hyperbolic manifolds
  • Lang conjectures
  • Kobayashi hyperbolicity

Dedicated to Hurşit Önsiper

Mathematics Subject Classification (2010). Primary 11E16 11E41; Secondary 11R29.

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Correspondence to Ayberk Zeytin .

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Zeytin, A. (2017). Class Number Problems and Lang Conjectures. In: Mourtada, H., Sarıoğlu, C., Soulé, C., Zeytin, A. (eds) Algebraic Geometry and Number Theory . Progress in Mathematics, vol 321. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-47779-4_7

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