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2002•Mathematics of ComputationOpen access

The tame kernel of imaginary quadratic fields with class number 2 or 3

Hong You, Sheng Chen

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Abstract

This paper presents improved bounds for the norms of exceptional finite places of the group K 2 O F K_2 O_F , where F F is an imaginary quadratic field of class number 2 or 3. As an application we show that K 2 Z [ − 10 ] = 1 K_{2}Z[\sqrt {-10}]=1 .

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This paper presents improved bounds for the norms of exceptional finite places of the group K 2 O F K_2 O_F , where F F is an imaginary quadratic field of class number 2 or 3. As an application we show that K 2 Z [ − 10 ] = 1 K_{2}Z[\sqrt {-10}]=1 .

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Available abstract

This paper presents improved bounds for the norms of exceptional finite places of the group K 2 O F K_2 O_F , where F F is an imaginary quadratic field of class number 2 or 3. As an application we show that K 2 Z [ − 10 ] = 1 K_{2}Z[\sqrt {-10}]=1 .

Key concepts: Mathematics, The Imaginary, Quadratic equation, Kernel (algebra), Class (philosophy), Quadratic field, Class field theory, Class number

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