We give explicit formulas for the 2-rank of the algebraic K-groups of quadratic number rings. A 4-rank formula for K2 of quadratic number rings given in [1] provides further information about the actual group structure. The K2 calculations are based on 2and 4rank formulas for Picard groups of quadratic number fields. These formulas are derived in a completely elementary way from the classical 2...

We study semi-stable ideal lattices coming from quadratic number fields. We prove that all ideal lattices of trace type from rings of integers of imaginary quadratic number fields are semi-stable. For real quadratic fields, we demonstrate infinite families of semi-stable and unstable ideal lattices, establishing explicit conditions on the canonical basis of an ideal that ensure stability; in pa...

We present a method for hierarchical data approximation using quadratic simplicial elements for domain decomposition and field approximation. Higher-order simplicial elements can approximate data better than linear elements. Thus, fewer quadratic elements are required to achieve similar approximation quality. We use quadratic basis functions and compute best quadratic simplicial spline approxim...

We construct lattices with quadratic structure over the integers in quadratic number fields having the property that the rank of the quadratic structure is constant and equal to the rank of the lattice in all reductions modulo maximal ideals. We characterize the case in which such lattices are free. The construction gives a representative of the genus of such lattices as an orthogonal sum of “s...

We study quadratic Lie algebras over a field K of null characteristic which admit, at the same time, a symplectic structure. We see that if K is algebraically closed every such Lie algebra may be constructed as the T∗-extension of a nilpotent algebra admitting an invertible derivation and also as the double extension of another quadratic symplectic Lie algebra by the one-dimensional Lie algebra...

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...

We propose a randomized polynomial time algorithm for computing nontrivial zeros of quadratic forms in 4 or more variables over Fq(t), where Fq is a finite field of odd characteristic. The algorithm is based on a suitable splitting of the form into two forms and finding a common value they both represent. We make use of an effective formula on the number of fixed degree irreducible polynomials ...

The best practical algorithm for class group computations in imaginary quadratic number fields (such as group structure, class number, discrete logarithm computations) is a variant of the quadratic sieve factoring algorithm. Paradoxical as it sounds, the principles of the number field sieve, in a strict sense, could not be applied to number field computations, yet. In this article we give an in...

A discussion of the field content of quadratic higher-derivative gravitation is presented, together with a new example of a massless spin-two field consistently coupled to gravity. The full quadratic gravity theory is shown to be equivalent to a canonical secondorder theory of a massive scalar field, a massive spin-two symmetric tensor field and gravity. The conditions showing that the tensor f...