Related papers: Monogenity in totally complex sextic fields, revis…

We complete the equisingular deformation classification of irreducible singular plane sextic curves. As a by-product, we also compute the fundamental groups of the complement of all but a few maximizing sextics.

We introduce a linearized version of group field theory. It can be viewed either as a group field theory over the additive group of a vector space or as an asymptotic expansion of any group field theory around the unit group element. We…

Fix a finite collection of primes $\{ p_j \}$, not containing $2$ or $3$. Using some observations which arose from attempts to solve the SIC-POVMs problem in quantum information, we give a simple methodology for constructing an infinite…

We prove a family of identities, expressing generating functions of powers of characteristic polynomials of permutations, as finite or infinite products. These generalize formulae first obtained in a study of the geometry/topology of…

An ideal is a classical object of study in the field of algebraic number theory. In maximal quadratic orders of number fields, ideals usually represented by the $\mathbb Z$-basis. This form of representation is used in most of the…

Power series are introduced that are simultaneously convergent for all real and p-adic numbers. Our expansions are in some aspects similar to those of exponential, trigonometric, and hyperbolic functions. Starting from these series and…

The paper is devoted to the problem of finding free generators in the fields of invariants for actions of unipotent groups on affine varieties. We consider the case when the unipotent group is the unipotent radical in an arbitrary parabolic…

Shift registers/Primitive polynomials find applications in various branches of Mathematics, Coding Theory and Cryptography. Matrix analogues of primitive polynomials do exist. In this paper, an algorithmic approach to generating all such…

We describe how Groebner bases can be used to solve the reduction problem for Feynman integrals, i.e. to construct an algorithm that provides the possibility to express a Feynman integral of a given family as a linear combination of some…

A general integral expression to transform power series is applied to $\arcsin{x}$ and its positive integer powers. We concentrate on the first to the fourth powers and obtain infinite classes of new power series involving central binomial…

In this paper we give an algorithm to determine all finite matrix groups over a number field. Our algorithm is based on the representation theory of finite groups.

We present a method to construct random model power grids that closely match statistical properties of a real power grid. The model grids are more difficult to partition than a real grid.

Some upper bounds for the number of monogenizations of quartic orders are established by considering certain classical Diophantine equations, namely index form equations in quartic number fields, and cubic and quartic Thue equations.

We show that an order in a quartic field has fewer than $3000$ essentially different generators as a $\mathbb Z$-algebra (and fewer than $200$ if the discriminant of the order is sufficiently large). This significantly improves the…

For an arbitrary cocompact hyperbolic Coxeter group G with finite generator set S and complete growth function P(x)/Q(x), we provide a recursion formula for the coefficients of the denominator polynomial Q(x) which allows to determine…

This paper presents fundamental algorithms for the computational theory of quadratic forms over number fields. In the first part of the paper, we present algorithms for checking if a given non-degenerate quadratic form over a fixed number…

In this paper we state and explain techniques useful for the computation of strong Gr\"obner and standard bases over Euclidean domains: First we investigate several strategies for creating the pair set using an idea by Lichtblau. Then we…

Let $\mathbb{K}$ be a field such that $char(\mathbb{K})\nmid k$ and $char(\mathbb{K})\nmid k+1$. We describe all $(k+1)$-potent matrices over the group of upper triangular matrix. In the case that $\mathbb{K}$ is a finite field we show how…

We construct parametric families of (monic) reducible polynomials having two roots very close to each other.

The Qth-power algorithm produces a useful canonical P-module presentation for the integral closures of certain integral extensions of $P:=\mathbf{F}[x_n,...,x_1]$, a polyonomial ring over the finite field $\mathbf{F}:=\mathbf{Z}_q$ of $q$…