### 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 |
---|---|

Pages (from-to) | 1207-1212 |

Number of pages | 6 |

Journal | Mathematics of Computation |

Volume | 69 |

Issue number | 231 |

Publication status | Published - 2000 Jul |

### Fingerprint

### Keywords

- Computation
- Siegel modular functions
- Unit groups

### ASJC Scopus subject areas

- Algebra and Number Theory
- Applied Mathematics
- Computational Mathematics

### Cite this

*Mathematics of Computation*,

*69*(231), 1207-1212.

**On a unit group generated by special values of Siegel modular functions.** / Fukuda, T.; Komatsu, Keiichi.

Research output: Contribution to journal › Article

*Mathematics of Computation*, vol. 69, no. 231, pp. 1207-1212.

}

TY - JOUR

T1 - On a unit group generated by special values of Siegel modular functions

AU - Fukuda, T.

AU - Komatsu, Keiichi

PY - 2000/7

Y1 - 2000/7

N2 - 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 k6 of ℚ(exp(2πi/5)) modulo 6 with full rank by special values of Siegel modular functions and circular units. We note that k6 = 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.

AB - 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 k6 of ℚ(exp(2πi/5)) modulo 6 with full rank by special values of Siegel modular functions and circular units. We note that k6 = 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.

KW - Computation

KW - Siegel modular functions

KW - Unit groups

UR - http://www.scopus.com/inward/record.url?scp=0034381448&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034381448&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0034381448

VL - 69

SP - 1207

EP - 1212

JO - Mathematics of Computation

JF - Mathematics of Computation

SN - 0025-5718

IS - 231

ER -