A143746 The number of totally real number fields of degree n with definite Eichler orders <=2.

1, 39, 47, 108, 37, 40, 4, 3

Offset

1,2

Comments

By the Odlyzko bounds, there are only finitely many such fields and they have been explicitly enumerated (by Voight) and no field satisfying the bound with n => 9, for a total of 279 fields. Kirschmer and Voight (pp. 26-27) also enumerate the ideal classes explicitly, Abstract: We provide algorithms to count and enumerate representatives of the (right) ideal classes of an Eichler order in a quaternion algebra defined over a number field. We analyze the run time of these algorithms and consider several related problems, including the computation of two-sided ideal classes, isomorphism classes of orders, connecting ideals for orders and ideal principalization. We conclude by giving the complete list of definite Eichler orders with class number at most 2.

Links

Table of n, a(n) for n=1..8.

Markus Kirschmer and John Voight, Algorithmic enumeration of ideal classes for quaternion orders, arXiv:0808.3833 [math.NT]

John Voight, Enumeration of totally real number fields of bounded root discriminant, Algorithmic number theory, eds. Alfred van der Poorten and Andreas Stein, Lecture notes in computer science, vol. 5011, Springer, Berlin, 2008, 268-281.

Crossrefs

Sequence in context: A252712 A252711 A046512 * A064399 A235151 A050439

Adjacent sequences: A143743 A143744 A143745 * A143747 A143748 A143749

Keyword

nonn,fini,full

Author

Jonathan Vos Post, Aug 30 2008

Status

approved