A subgroup of Î“ which contains some principal congruence subgroup is called a congruence subgroup. The level of a congruence subgroup G is the smallest N such that Î“(N) âŠ‚ G. The literature onâ€¦ (More)

Let k be a p-adic field. It is well-known that k has only finitely many extensions of a given finite degree. Krasner has given formulae for the number of extensions of a given degree andâ€¦ (More)

A new invariant of number fields, called group of logarithmic classes, was introduced by J. -F. Jaulent in 1994 [Jaulent 94]. The interest in the arithmetic of logarithmic classes comes from itsâ€¦ (More)

We present an algorithm for the computation of the discrete logarithm in logarithmic `-Class Groups. This is applied to the calculation to the `-rank of the wild kernel WK2 of a number field F and inâ€¦ (More)

We present an algorithm for factoring polynomials over local fields, in which the Montes algorithm is combined with elements from Zassenhaus Round Four algorithm. This algorithm avoids theâ€¦ (More)

Let f (x) be a separable polynomial over a local field. The Montes algorithm computes certain approximations to the different irreducible factors of f (x), with strong arithmetic properties. In thisâ€¦ (More)

In recent years the computer algebra system KASH/KANT for number theory has evolved considerably. We present its new features and introduce the related components, QaoS (Querying Algebraic Objectsâ€¦ (More)

Let K be a a global field and O be an order of K. We develop algorithms for the computation of the unit group of residue class rings for ideals in O. As an application we show how to compute the unitâ€¦ (More)

We present an algorithm for computing the 2-group e C` res F of narrow logarithmic divisor classes of degree 0 for number fields F . As an application, we compute in some cases the 2-rank of the wildâ€¦ (More)