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

Solving polynomial systems arising from applications is frequently made easier by the structure of the systems. Weighted homogeneity (or quasi-homogeneity) is one example of such a structure: given a system of weights…

This paper is concerned with the question of whether geometric structures such as cell complexes can be used to simultaneously describe the minimal free resolutions of all powers of a monomial ideal. We provide a full answer in the case of…

This paper demonstrates that extremal ideals can be used to great effect to compute integral closures of powers and symbolic powers of square-free monomial ideals. We show that the generators of these powers are images of the generators of…

We adapt a known technique for searching for ideal classes of arbitrary order and then apply it to three families of number fields. We show that a family of cyclic sextic number fields has infinitely many fields in it that contain a…

Exploratory variational pseudopotential density functional calculations are performed for the electronic properties of many-electron systems in the 3D cartesian coordinate grid (CCG). The atom-centered localized gaussian basis set,…

In this paper, we propose a procedure for constructing an infinite number of families of solutions of given linear differential equations with partial derivatives with constant coefficients. We use monogenic functions that are defined on…

Deciding whether an ideal of a number field is principal and finding a generator is a fundamental problem with many applications in computational number theory. For indefinite quaternion algebras, the decision problem reduces to that in the…

Analytical explorations on complex networks and cubes (i.e., multi-dimensional datasets) are currently two separate research fields with different strategies. To gain more insights into cube dynamics via unique network-domain methodologies…

Let $U/L$ be a finite abelian extension of number fields. We first construct a universal primitive generator of $U$ over $L$ whose relative trace to any intermediate field $F$ becomes a generator of $F$ over $L$, too. We also develop a…

Exact solutions construction in scalar fields cosmology is of growing interest. In this work we review the results which obtained with the help of one of the most effective method. Namely, the method of generating functions for exact…

A perturbative approach to quantum field theory involves the computation of loop integrals, as soon as one goes beyond the leading term in the perturbative expansion. First I review standard techniques for the computation of loop integrals.…

We extend several predecessor works on even sextic monogenic polynomials. In particular, we prove a conjecture of Lenny Jones, thereby classifying even sextic monogenic polynomials with cyclic Galois group. This result is key to completing…

In this paper, we study the generating function of cyclically fully commutative elements in Coxeter groups, which are elements such that any cyclic shift of theirs reduced decompositions remains a reduced expression of a fully commutative…

We construct explicit geometric models for and compute the fundamental groups of all plane sextics with simple singularities only and with at least one type $\bold E_8$ singular point. In particular, we discover four new sextics with…

We present new computational results for symplectic monodromy groups of hypergeometric differential equations. In particular, we compute the arithmetic closure of each group, sometimes justifying arithmeticity. The results are obtained by…

We obtain divisibility conditions on the multiplicative orders of elements of the form $\zeta + \zeta^{-1}$ in a finite field by exploiting a link to the arithmetic of real quadratic fields.

Let $A$ be a Dedekind domain, $K$ the fraction field, $\p$ a non-zero prime ideal of $A$, and $K_\pp$ the completion of $K$ with respect to the $\p$-adic topology. At the input of a monic irreducible separable polynomial, $f(x)\in A[x]$,…

We compute the fundamental groups of five maximizing sextics with double singular points only; in four cases, the groups are as expected. The approach used would apply to other sextics as well, given their equations.

We study a multi-parametric family of quadratic algebras in four generators, which includes coordinate algebras of noncommutative four-planes and, as quotient algebras, noncommutative three spheres. Particular subfamilies comprise Sklyanin…

We introduce two families of generators (functions) $\mathcal{G}$ that consist of entire and meromorphic functions enjoying a certain periodicity property and contain the classical Gaussian and hyperbolic secant generators. Sharp results…