arXiv subjects

Beata Rothkegel

Publications and source records attributed to Beata Rothkegel.

3 recordsLinked to original sources

arXiv2022

Computing the Length of Sum of Squares and Pythagoras Element in a Global Field

This paper presents algorithms for computing the length of a sum of squares and a Pythagoras element in a global field $K$ of characteristic different from $2$. In the first part of the paper, we present algorithms for computing the length in a non-dyadic and dyadic (if $K$ is a number field) completion of $K$. These two algorithms serve as subsidiary steps for computing lengths in global fields. In the second part of the paper we present a procedure for constructing an element whose length equals the Pythagoras number of a global field, termed a Pythagoras element.

math.NT↗

arXiv2021

The anisotropic part of a quadratic form over a number field

It is well known that every non-degenerate quadratic form admits a decomposition into an orthogonal sum of its anisotropic part and a hyperbolic form. This decomposition is unique up to isometry. In this paper we present an algorithm for constructing an anisotropic part of a given form with coefficients in an arbitrary number field.

math.NT↗

arXiv2018

Wild sets in global function fields

Given a self-equivalence of a global function field, its wild set is the set of points where the self-equivalence fails to preserve parity of valuation. In this paper we describe structure of finite wild sets.

math.NT↗