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(1998 / vol.1 / no.1)
Recent Results on Arithmetic of the Simplest Cubic Fields
Hyun Kwang Kim
Pages. 46-51     



The purpose of this paper is to survey recent results on arithmetic
properties of the simplest cubic fields. First, we introduce the notion of the simplest cubic
fields and develop basic materials. Next, we shall discuss arithmetic
of the simplest cubic fields such as computation of class number, class
number problem, computation of special values of zeta function, and structure
of ideal class group.



1. Simplest cubic fields
2. The class numbers of the simplest cubic fields
3. Class number problem for the simplest cubic fields
4. Values of zeta functions



Simplest cubic fields, Dedekind zeta function, class number formula, p-adic class number formula, elliptic curve, 2-rank of ideal class group



11R16, 11R42