On a unit group generated by special values of Siegel modular functions
On a unit group generated by special values of Siegel modular functions
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关于由Siegel模函数的特殊值生成的单位群
DOI：
10.1090/s0025-5718-99-01118-7
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
K. Komatsu
中科院分区：
文献类型：
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作者：
T. Fukuda;K. Komatsu
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 hyper-elliptic 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.
