The Stickelberger element of an imaginary quadratic field

The Stickelberger element of an imaginary quadratic field

L - Functions and Class Numbers of Imaginary Quadratic Fields and of Quadratic Extensions of an Imaginary Quadratic Field

Starting from the analytic class number formula involving its Lfunction, we first give an expression for the class number of an imaginary quadratic field which, in the case of large discriminants, provides us with a much more powerful numerical technique than that of counting the number of reduced definite positive binary quadratic forms, as has been used by Buell in order to compute his class ...

Imaginary Quadratic

is called the 2-class field tower of k. If n is the minimal integer such that kn = kn+1, then n is called the length of the tower. If no such n exists, then the tower is said to be of infinite length. At present there is no known decision procedure to determine whether or not the (2-)class field tower of a given field k is infinite. However, it is known by group theoretic results (see [2]) that...

On 2-class field towers of imaginary quadratic number fields

For a number field k, let k1 denote its Hilbert 2-class field, and put k2 = (k1)1. We will determine all imaginary quadratic number fields k such that G = Gal(k2/k) is abelian or metacyclic, and we will give G in terms of generators and relations.

Class numbers in the imaginary quadratic field and the 1/f noise of an electron gas

Partition functions Z(x) of statistical mechanics are generally approximated by integrals. The approximation fails in small cavities or at very low temperature, when the ratio x between the energy quantum and thermal energy is larger or equal to unity. In addition, the exact calculation, which is based on number theoretical concepts, shows excess low frequency noise in thermodynamical quantitie...