The situation changed when Gauss used Gauss sums to show that quadratic fields are subfields of cyclotomic fields, and implicitly deduced quadratic reciprocity from a reciprocity theorem for cyclotomic fields.
32.
The original Gauss class number problem for imaginary quadratic fields is significantly different and easier than the modern statement : he restricted to even discriminants, and allowed non-fundamental discriminants.
33.
The complete answer to this question has been completely worked out only when "'K "'is an imaginary quadratic field or its generalization, a CM-field.
34.
Peter Gustav Lejeune Dirichlet published a proof of the class number formula for quadratic fields in 1839, but it was stated in the language of quadratic forms rather than classes of ideals.
35.
The description is in terms of Frobenius elements, and generalises in a far-reaching way the quadratic reciprocity law that gives full information on the decomposition of prime numbers in quadratic fields.
36.
As an example, if " K " is a quadratic field, the rank is 1 if it is a real quadratic field, and 0 if an imaginary quadratic field.
37.
As an example, if " K " is a quadratic field, the rank is 1 if it is a real quadratic field, and 0 if an imaginary quadratic field.
38.
As an example, if " K " is a quadratic field, the rank is 1 if it is a real quadratic field, and 0 if an imaginary quadratic field.
39.
The tensor product of End ( " A " ) with the rational number field "'Q "', should contain a commutative subring of order in an imaginary quadratic field.
40.
Arithmetical aspects of the theory of binary quadratic forms are related to the arithmetic of quadratic fields and have been much studied, notably, by Gauss in Section V of " Disquisitiones Arithmeticae ".
How to say quadratic field in Hindi and what is the meaning of quadratic field in Hindi? quadratic field Hindi meaning, translation, pronunciation, synonyms and example sentences are provided by Hindlish.com.
