Selberg integral over local fields

Semigroups over Local fields

Let G be a 1-connected, almost-simple Lie group over a local field and S a subsemigroup of G with non-empty interior. The action of the regular hyperbolic elements in the interior of S on the flag manifold G/P and on the associated Euclidean building allows us to prove that the invariant control set exists and is unique. We also provide a characterization of the set of transitivity of the contr...

Constructing class fields over local fields

Let K be a p-adic field. We give an explicit characterization of the abelian extensions of K of degree p by relating the coefficients of the generating polynomials of extensions L/K of degree p to the exponents of generators of the norm group NL/K(L ∗). This is applied in an algorithm for the construction of class fields of degree pm, which yields an algorithm for the computation of class field...

Integral point sets over finite fields

We consider point sets in the affine plane Fq where each Euclidean distance of two points is an element of Fq . These sets are called integral point sets and were originally defined in m-dimensional Euclidean spaces Em. We determine their maximal cardinality I(Fq , 2). For arbitrary commutative rings R instead of Fq or for further restrictions as no three points on a line or no four points on a...

Factoring Polynomials over Local Fields

Factoring Polynomials over Local Fields