Geodesic
Computing Polynomials of the Ramanujan tn Class Invariants
Canadian mathematical bulletin, Tome 52 (2009) no. 4, pp. 583-597

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DOI

We compute the minimal polynomials of the Ramanujan values ${{t}_{n}}$ , where $n\,\equiv \,11\,\bmod \,24$ , using the Shimura reciprocity law. These polynomials can be used for defining the Hilbert class field of the imaginary quadratic field $\mathbb{Q}\left( \sqrt{-n} \right)$ and have much smaller coefficients than the Hilbert polynomials.
DOI : 10.4153/CMB-2009-058-6
Mots-clés : 11R29, 33E05, 11R20 
Konstantinou, Elisavet; Kontogeorgis, Aristides. Computing Polynomials of the Ramanujan tn Class Invariants. Canadian mathematical bulletin, Tome 52 (2009) no. 4, pp. 583-597. doi: 10.4153/CMB-2009-058-6
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     author = {Konstantinou, Elisavet and Kontogeorgis, Aristides},
     title = {Computing {Polynomials} of the {Ramanujan} tn {Class} {Invariants}},
     journal = {Canadian mathematical bulletin},
     pages = {583--597},
     year = {2009},
     volume = {52},
     number = {4},
     doi = {10.4153/CMB-2009-058-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2009-058-6/}
}
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