Special values of Siegel modular functions and Jacobian variety

构造了一类代数整数αm作为某个四次域的射线类域中二元θ函数的特殊值，并结合分圆单位与指数函数、椭圆单位与椭圆函数之间的关系，研究了αm中出现的素数i的一个性质。研究了复乘法阿贝尔簇的Mordell-Weil秩与ZLP扩张的Iwasawa λ-不变量之间的关系.

We construct certain algebraic integers αm as special values of two variable theta functions in the ray class field of a certain quartic field modulo 2m, and study a property of prime i deals which appear in αm in connection to the relationships between cyclotomic units and exponential functions and between elliptic units and elliptic functions, Moreover, we study a relationship between the Mordell-Weil rank of an abelian variety with complex multiplication and the Iwasawa λ-invariant of a certain ZLP-extension.