Computing polynomials of the Ramanujan $\mathbf{t_n}$ class invariants

Elisavet Konstantinou; Aristides Kontogeorgis

Computing polynomials of the Ramanujan $\mathbf{t_n}$ class invariants

Number Theory 2007-05-23 v1

Authors: Elisavet Konstantinou , Aristides Kontogeorgis

Abstract

We compute the minimal polynomials of the Ramanujan values $t_n$ , where $n\equiv 11 \mod 24$ , using 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.

Keywords

ramanujan identities and series

Cite

@article{arxiv.math/0610372,
  title  = {Computing polynomials of the Ramanujan $\mathbf{t_n}$ class invariants},
  author = {Elisavet Konstantinou and Aristides Kontogeorgis},
  journal= {arXiv preprint arXiv:math/0610372},
  year   = {2007}
}

Comments

To appear in Canadian Math. Bulletin

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