A duality based proof of the combinatorial nullstellensatz.
A fast numerical test of multivariate polynomial positiveness with applications
The paper presents a simple method to check a positiveness of symmetric multivariate polynomials on the unit multi-circle. The method is based on the sampling polynomials using the fast Fourier transform. The algorithm is described and its possible applications are proposed. One of the aims of the paper is to show that presented algorithm is significantly faster than commonly used method based on the semi-definite programming expression.
A Galois theory with stable units for simplicial sets.
A GAP package for braid orbit computation and applications.
A generalisation of the Cassel-Tate pairing.
A generalization of a result on integers in metacyclic extensions
Let p be an odd prime and let c be an integer such that c>1 and c divides p-1. Let G be a metacyclic group of order pc and let k be a field such that pc is prime to the characteristic of k. Assume that k contains a primitive pcth root of unity. We first characterize the normal extensions L/k with Galois group isomorphic to G when p and c satisfy a certain condition. Then we apply our characterization to the case in which k is an algebraic number field with ring of integers ℴ, and, assuming some...
A generalization of a second irreducibility theorem of I. Schur
A generalization of a third irreducibility theorem of I. Schur
A generalization of Ostrowski' theorem on ultrametric inequalities.
A generalization of Schinzel's theorem on radical extensions of fields and an application
A generalization of the Gauss-Lucas theorem
Given a set of points in the complex plane, an incomplete polynomial is defined as the one which has these points as zeros except one of them. The classical result known as Gauss-Lucas theorem on the location of zeros of polynomials and their derivatives is extended to convex linear combinations of incomplete polynomials. An integral representation of convex linear combinations of incomplete polynomials is also given.
A generalization of the Hasse-Arf theorem.
A generalization of the method of global relation.
A generalization of the sizes of differential equations and its applications to -function theory
A geometric maximization problem
A Hasse principle for two dimensional global fields.
A Hauptsatz of L. E. Dickson and Artin-Schreier extensions.
A hypercomplex proof of the Jordan-Kronecker's “Principle of reduction”
A model-theoretic transfer theorem for henselian valued fields.
A monogenic Hasse-Arf theorem
I extend the Hasse–Arf theorem from residually separable extensions of complete discrete valuation rings to monogenic extensions.