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

Nous construisons les unités de Minkowski du corps de classes de rayon modulo 6, k 6 , de ℚ(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 /ℚ) 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.

Using the special values of Siegel modular functions, we construct Minkowski units for the ray class field k 6 of ℚ(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 /ℚ) for the special values. Futhermore we construct the full unit group of k 6 using modular and circular units under the GRH.

@article{JTNB_2003__15_1_133_0,
     author = {Fukuda, Takashi and Komatsu, Keiichi},
     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},
     mrnumber = {2019006},
     zbl = {02058859},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2003__15_1_133_0/}
}
TY  - JOUR
AU  - Fukuda, Takashi
AU  - Komatsu, Keiichi
TI  - On Minkowski units constructed by special values of Siegel modular functions
JO  - Journal de théorie des nombres de Bordeaux
PY  - 2003
SP  - 133
EP  - 140
VL  - 15
IS  - 1
PB  - Université Bordeaux I
UR  - http://www.numdam.org/item/JTNB_2003__15_1_133_0/
LA  - en
ID  - JTNB_2003__15_1_133_0
ER  - 
%0 Journal Article
%A Fukuda, Takashi
%A Komatsu, Keiichi
%T On Minkowski units constructed by special values of Siegel modular functions
%J Journal de théorie des nombres de Bordeaux
%D 2003
%P 133-140
%V 15
%N 1
%I Université Bordeaux I
%U http://www.numdam.org/item/JTNB_2003__15_1_133_0/
%G en
%F JTNB_2003__15_1_133_0
Fukuda, Takashi; Komatsu, Keiichi. On Minkowski units constructed by special values of Siegel modular functions. Journal de théorie des nombres de Bordeaux, Tome 15 (2003) no. 1, pp. 133-140. http://www.numdam.org/item/JTNB_2003__15_1_133_0/

[1] T. Fukuda, K. Komatsu, On a unit group generated by special values of Siegel modular functions. Math. Comp. 69 (2000), 1207-1212. | MR | Zbl

[2] J. Igusa, Modular forms and projective invariants. Amer. J. Math. 89 (1967), 817-855. | MR | Zbl

[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

[4] Kenzo Komatsu, An integral basis of the algebraic number field ℚ [ a ℓ , 1 ℓ ) , J. Reine Angew. Math. 288 (1976), 152-154. | Zbl

[5] G. Shimura, Theta functions with complex multiplication. Duke Math. J. 43 (1976), 673-696. | MR | Zbl