Special values of Siegel modular functions and Jacobian variety

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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.