1. It uses Lucas sequences to perform exponentiation in a quadratic field . 2. The following table shows some orders of small discriminant of quadratic fields . 3. It covers elementary number theory, Dirichlet's theorem, and quadratic fields . 4. The theory for real quadratic fields is essentially the theory of Pell's equation. 5. This occurs if and only if the class number of the corresponding quadratic field is one. 6. Before that in his dissertation used Hilbert modular forms to study abelian extensions of real quadratic fields . 7. This result is ineffective, as indeed was the result on quadratic fields on which it built. 8. Although the quadratic integers belonging to a given quadratic field form a minimal polynomial of degree four. 9. Chapter 5 contains Dirichlet's derivation of the class number formula for real and imaginary quadratic fields . 10. While all quadratic fields are monogenic, already among cubic fields there are many that are not monogenic.
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