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

Abstract. There has been important progress in constructing units and Sunits 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(2i/5)) modulo 6 with full rank by special values of Siegel modular functions and circular units. We note that k6 = Q(exp(2i/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.

• Type: Journal
• Year: 2000
• Where: MOC
• Authors: Takashi Fukuda, Keiichi Komatsu
• Keywords: Important Progress, MOC 2000, Ray Class Field, Special Values