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Diophantine equations over ℂ(t) and complex multiplication

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Part of the Lecture Notes in Mathematics book series (LNM,volume 751)

Abstract

The diophantine equations tx3−(t−1)y2=1 (or x) can be completely solved in ℂ(t) by complex multiplication in the ring of sixth (or fourth) roots of unity. Relations to well-known diophantine equations in Φ are indicated.

Keywords

  • Complex Multiplication
  • Elliptic Curf
  • Elliptic Function
  • Function Field
  • Polynomial Identity

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1979 Springer-Verlag

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Cohn, H. (1979). Diophantine equations over ℂ(t) and complex multiplication. In: Nathanson, M.B. (eds) Number Theory Carbondale 1979. Lecture Notes in Mathematics, vol 751. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062702

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  • DOI: https://doi.org/10.1007/BFb0062702

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09559-0

  • Online ISBN: 978-3-540-34852-8

  • eBook Packages: Springer Book Archive