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Computing Polynomials of the Ramanujan $t_n$ Class Invariants

  Published:2009-12-01
 Printed: Dec 2009
  • Elisavet Konstantinou
  • Aristides Kontogeorgis
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Abstract

We compute the minimal polynomials of the Ramanujan values $t_n$, where $n\equiv 11 \mod 24$, using the Shimura reciprocity law. These polynomials can be used for defining the Hilbert class field of the imaginary quadratic field $\mathbb{Q}(\sqrt{-n})$ and have much smaller coefficients than the Hilbert polynomials.
MSC Classifications: 11R29, 33E05, 11R20 show english descriptions Class numbers, class groups, discriminants
Elliptic functions and integrals
Other abelian and metabelian extensions
11R29 - Class numbers, class groups, discriminants
33E05 - Elliptic functions and integrals
11R20 - Other abelian and metabelian extensions
 

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