On Minkowski units constructed by special values of Siegel modular functions
Journal de Théorie des Nombres de Bordeaux, Volume 15 (2003) no. 1, pp. 133-140.

Using the special values of Siegel modular functions, we construct Minkowski units for the ray class field k 6 of (exp(2πi/5)) modulo 6. Our work is based on investigating the prime decomposition of the special values and describing explicitly the action of the Galois group G(k 6 /) for the special values. Futhermore we construct the full unit group of k 6 using modular and circular units under the GRH.

Nous construisons les unités de Minkowski du corps de classes de rayon modulo 6, k 6 , de (exp(2πi/5)) en utilisant les valeurs spéciales des fonctions modulaires de Siegel. Notre travail utilise la décomposition en idéaux premiers des valeurs spéciales et la description de l’action du groupe de Galois G(k 6 /) sur ces valeurs spéciales. De plus, sous GRH, nous décrivons entièrement le groupe des unités de k 6 à partir unités modulaires et des unités circulaires.

@article{JTNB_2003__15_1_133_0,
     author = {Takashi Fukuda and Keiichi Komatsu},
     title = {On {Minkowski} units constructed by special values of {Siegel} modular functions},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {133--140},
     publisher = {Universit\'e Bordeaux I},
     volume = {15},
     number = {1},
     year = {2003},
     doi = {10.5802/jtnb.392},
     zbl = {02058859},
     mrnumber = {2019006},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.392/}
}
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Takashi Fukuda; Keiichi Komatsu. On Minkowski units constructed by special values of Siegel modular functions. Journal de Théorie des Nombres de Bordeaux, Volume 15 (2003) no. 1, pp. 133-140. doi : 10.5802/jtnb.392. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.392/

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[3] Keichii Komatsu, Construction of a normal basis by special values of Siegel modular functions. Proc. Amer. Math. Soc. 128 (2000), 315-323. | MR | Zbl

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