### Abstract

There has been important progress in constructing units and S-units associated to curves of genus 2 or 3. These approaches are based mainly on the consideration of properties of Jacobian varieties associated to hyperelliptic curves of genus 2 or 3. In this paper, we construct a unit group of the ray class field k_{6} of ℚ(exp(2πi/5)) modulo 6 with full rank by special values of Siegel modular functions and circular units. We note that k_{6} = ℚ(exp(2πi/15), ^{5}√-24). Our construction of units is number theoretic, and closely based on Shimura's work describing explicitly the Galois actions on the special values of theta functions.

Original language | English |
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Pages (from-to) | 1207-1212 |

Number of pages | 6 |

Journal | Mathematics of Computation |

Volume | 69 |

Issue number | 231 |

Publication status | Published - 2000 Jul |

### Keywords

- Computation
- Siegel modular functions
- Unit groups

### ASJC Scopus subject areas

- Algebra and Number Theory
- Applied Mathematics
- Computational Mathematics

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## Cite this

Fukuda, T., & Komatsu, K. (2000). On a unit group generated by special values of Siegel modular functions.

*Mathematics of Computation*,*69*(231), 1207-1212.