On Minkowski units constructed by special values of Siegel modular functions

Takashi Fukuda; Keiichi Komatsu

Journal de théorie des nombres de Bordeaux (2003)

  • Volume: 15, Issue: 1, page 133-140
  • ISSN: 1246-7405

Abstract

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Using the special values of Siegel modular functions, we construct Minkowski units for the ray class field k 6 of ℚ ( e x p ( 2 π i / 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.

How to cite

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Fukuda, Takashi, and Komatsu, Keiichi. "On Minkowski units constructed by special values of Siegel modular functions." Journal de théorie des nombres de Bordeaux 15.1 (2003): 133-140. <http://eudml.org/doc/249104>.

@article{Fukuda2003,
abstract = {Using the special values of Siegel modular functions, we construct Minkowski units for the ray class field $k_6$ of $\mathbb \{Q\}(exp(2\pi i/5))$ modulo $6$. Our work is based on investigating the prime decomposition of the special values and describing explicitly the action of the Galois group $G(k_6/ \mathbb \{Q\})$ for the special values. Futhermore we construct the full unit group of $k_6$ using modular and circular units under the GRH.},
author = {Fukuda, Takashi, Komatsu, Keiichi},
journal = {Journal de théorie des nombres de Bordeaux},
language = {eng},
number = {1},
pages = {133-140},
publisher = {Université Bordeaux I},
title = {On Minkowski units constructed by special values of Siegel modular functions},
url = {http://eudml.org/doc/249104},
volume = {15},
year = {2003},
}

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
PB - Université Bordeaux I
VL - 15
IS - 1
SP - 133
EP - 140
AB - Using the special values of Siegel modular functions, we construct Minkowski units for the ray class field $k_6$ of $\mathbb {Q}(exp(2\pi i/5))$ modulo $6$. Our work is based on investigating the prime decomposition of the special values and describing explicitly the action of the Galois group $G(k_6/ \mathbb {Q})$ for the special values. Futhermore we construct the full unit group of $k_6$ using modular and circular units under the GRH.
LA - eng
UR - http://eudml.org/doc/249104
ER -

References

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  1. [1] T. Fukuda, K. Komatsu, On a unit group generated by special values of Siegel modular functions. Math. Comp.69 (2000), 1207-1212. Zbl1037.11043MR1651753
  2. [2] J. Igusa, Modular forms and projective invariants. Amer. J. Math.89 (1967), 817-855. Zbl0159.50401MR229643
  3. [3] Keichii Komatsu, Construction of a normal basis by special values of Siegel modular functions. Proc. Amer. Math. Soc.128 (2000), 315-323. Zbl0965.11043MR1707153
  4. [4] Kenzo Komatsu, . J. Reine Angew. Math.288 (1976), 152-154. Zbl0335.12016
  5. [5] G. Shimura, Theta functions with complex multiplication. Duke Math. J.43 (1976), 673-696. Zbl0371.14022MR424705

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