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1972•Transactions of the American Mathematical SocietyOpen access

Relative imaginary quadratic fields of class number $1$ or $2$

Larry Joel Goldstein

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Abstract

Let K be a normal totally real algebraic number field. It is shown how to effectively classify all totally imaginary quadratic extensions of class number 1. Let K be a real quadratic field of class number 1, whose fundamental unit has norm $- 1$. Then it is shown how to effectively classify all totally imaginary quadratic extensions of class number 2.

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Let K be a normal totally real algebraic number field. It is shown how to effectively classify all totally imaginary quadratic extensions of class number 1. Let K be a real quadratic field of class number 1, whose fundamental unit has norm $- 1$. Then it is shown how to effectively classify all totally imaginary quadratic extensions of class number 2.

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Available abstract

Let K be a normal totally real algebraic number field. It is shown how to effectively classify all totally imaginary quadratic extensions of class number 1. Let K be a real quadratic field of class number 1, whose fundamental unit has norm $- 1$. Then it is shown how to effectively classify all totally imaginary quadratic extensions of class number 2.

Key concepts: Mathematics, Class number, Quadratic field, Quadratic equation, The Imaginary, Algebraic number field, Class (philosophy), Binary quadratic form

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