Some euclidean properties for real quadratic fields

On the Euclidean minimum of some real number fields par

General methods from [3] are applied to give good upper bounds on the Euclidean minimum of real quadratic fields and totally real cyclotomic fields of prime power discriminant.

Euclidean Ideals in Quadratic Imaginary Fields

— We classify all quadratic imaginary number fields that have a Euclidean ideal class. There are seven of them, they are of class number at most two, and in each case the unique class that generates the class-group is moreover norm-Euclidean.

Real Quadratic Number Fields

a4 + 1 a5 + .. . will see that a less wasteful notation, say [ a0 , a1 , a2 , . . . ] , is needed to represent it. Anyone attempting to compute the truncations [ a0 , a1 , . . . , ah ] = ph/qh will be delighted to notice that the definition [ a0 , a1 , . . . , ah ] = a0 + 1/[ a1 , . . . , ah ] immediately implies by induction on h that there is a correspondence ( a0 1 1 0 ) ( a1 1 1 0 ) · · · (...

Geometric Invariants for Real Quadratic Fields

To an ideal class of a real quadratic field we associate a certain surface. This surface, which is a new geometric invariant, has the usual modular closed geodesic as its boundary. Furthermore, its area is determined by the length of an associated backward continued fraction. We study the distribution properties of this surface on average over a genus. In the process we give an extension and re...

Hecke Eigenvalues for Real Quadratic Fields