Related papers: An invariant for difference field extensions

Generalizing the noncommutative harmonic oscillator construction, we propose a new extension of quantum field theory based on the concept of "noncommutative fields". Our description permits to break the usual particle-antiparticle…

We discuss and relate finiteness conditions for certain field invariants which are studied in quadratic form theory. This includes the $u$-invariant, the reduced stability index and the symbol lengths for Galois cohomology groups with…

We give an algorithm that constructs a minimal set of polynomials defining all extension of a $(\pi)$-adic field with given, inertia degree, ramification index, discriminant, ramification polygon, and residual polynomials of the segments of…

We survey various Alexander-type invariants of plane curve complements, with an emphasis on obstructions on the type of groups that can arise as fundamental groups of complements to complex plane curves. Also included are some new…

Estimates for invariant distances of convexifiable, $\C$-convexifiable and planar domains are given.

In this paper we look at the automorphisms of the multiplicative group of finite nearfields. We find partial results for the actual automorphism groups. We find counting techniques for the size of all finite nearfields. We then show that…

We define a notion of r-generalized column distances for the j-truncation of a convolutional code. Taking the limit as j tends to infinity allows us to define r-generalized column distances of a convolutional code. We establish some…

We investigate diagonal forms of degree $d$ over the function field $F$ of a smooth projective $p$-adic curve: if a form is isotropic over the completion of $F$ with respect to each discrete valuation of $F$, then it is isotropic over…

We establish bounds on a finite separable extension of function fields in terms of the relative class number, thus reducing the problem of classifying extensions with a fixed relative class number to a finite computation. We also solve the…

In this paper we find the genus field of finite abelian extensions of the global rational function field. We introduce the term conductor of constants for these extensions and determine it in terms of other invariants. We study the…

We present an overview of a theory of complex dimensions of self-similar fractal strings, and compare this theory to the theory of varieties over a finite field from the geometric and the dynamical point of view. Then we combine the several…

This paper is devoted to the study of generalized differentiation properties of the infimal convolution. This class of functions covers a large spectrum of nonsmooth functions well known in the literature. The subdifferential formulas…

We study the semicontinuity of automorphism groups for perturbations of domains in complex space or in complex manifolds. We provide a new approach to the study of such results for domains having minimal boundary smoothness. The emphasis in…

In this article we establish certain variants of the Inverse Cluster Size problem. We introduce the notion of primitive extensions and establish the Primitive variant of the problem. Precisely, we prove the existence of primitive extensions…

We introduce a new type of distinct distances result: a lower bound on the number of distances between points on a line and points on a two-dimensional strip. This can be seen as a generalization of the well-studied problems of distances…

The unit Euclidean distance degree and the generic Euclidean distance degree are two well-studied invariants of projective varieties. These quantities measure the algebraic complexity of nearest-point problems on a variety, and in many…

Let $G$ be one of the classical groups of Lie rank $l$. We make a similar construction of a general extension field in differential Galois theory for $G$ as E. Noether did in classical Galois theory for finite groups. More precisely, we…

A novel method for computation of the discrete Fourier transform over a finite field with reduced multiplicative complexity is described. If the number of multiplications is to be minimized, then the novel method for the finite field of…

A classification of (countable) direct limits of finite dimensional involution simple associative algebras over an algebraically closed field of arbitrary characteristic is obtained. This also classifies the corresponding dimension groups.…

We introduce two spectral invariants of finite metric spaces, the $q$-spectrum and the transition $q$-spectrum, defined from similarity matrices. These invariants extend the adjacency and Laplacian spectra of graphs to general finite metric…