相关论文: Small Norms in Quadratic Fields

In this paper, we consider the degenerate Carlitz q-Bernoulli numbers and polynomials and we investigate some properties of those polynomials.

We study scalar field theory in one space and one time dimensions on a q-deformed space with static background. We write the Lagrangian and the equation of motion and solve it to the first order in $q-1$ where $q$ is the deformation…

Line fields on surfaces are a means to describe the nematic order that may pattern them. The least distorted nematic fields are called uniform, but they can only exist on surfaces with negative constant Gaussian curvature. To identify the…

We prove some positivity results on the coefficients in the complexified Hilbert polynomial of a semi-stable object. After applying these results on the classical slope stability conditions, we get sequences of quadratic inequalities for…

We determine the shapes of pure cubic fields and show that they fall into two families based on whether the field is wildly or tamely ramified (of Type I or Type II in the sense of Dedekind). We show that the shapes of Type I fields are…

Using the Ratios Conjecture, we write down precise formulas with lower order terms for the one and the two level densities of zeros of quadratic Dirichlet $L$--functions over function fields. We denote the various terms arising as Type-$0$,…

We use the method of vector fields to obtain a Liouville-type theorem for a class of quasilinear p-Laplace type equations with conormal boundary condition in the half space. These p-Laplace type equations are the subcritical case of the…

We construct a family of ideals representing ideal classes of order 2 in quadratic number fields and show that relations between their ideal classes are governed by certain cyclic quartic extensions of the rationals.

The recent progress in color BFKL-Regge phenomenology of small-x DIS on nucleons, pions and photons is reviewed

In this paper, we establish the explicit lower bound estimates for the rank of universal quadratic forms in some certain families of real cubic fields under the condition of density one. The more general results that represent all multiples…

A class of fourth--order neutral type difference equations with quasidifferences and deviating arguments is considered. Our approach is based on studying the considered equation as a system of a four--dimensional difference system. The…

A certain pattern of divergence of perturbative expansions in quantum field theories, related to their small and large momentum behaviour, is known as renormalons. We review formal and phenomenological aspects of renormalon divergence. We…

In this paper we considerably extend the class of known $\alpha$-minimizing hypercones using sub-calibration methods. Indeed, the improvement of previous results follows from a careful analysis of special cubic and quartic polynomials.

We calculate the exact values of the quasinormal frequencies for an electromagnetic field and a gravitational perturbation moving in $D$-dimensional de Sitter spacetime ($D \geq 4$). We also study the quasinormal modes of a real massive…

We study nematic equilibria on rectangular domains, in a reduced two-dimensional Landau-de Gennes framework. These reduced equilibria carry over to the three-dimensional framework at a special temperature. There is one essential model…

We characterise Newton polytopes of nondegenerate quadratic forms and Newton polyhedra of Morse singularities.

In this paper we make a Gaussian integer version of the Erd\H{o}s-Straus conjecture and we solve the Erd\H{o}s-Straus diophantine equation over the rings of integers of norm-Euclidean quadratic fields.

We introduce methods to study the combinatorics of the normal form of large random elements in Artin-Tits monoids. These methods also apply in an axiomatic framework that encompasses other monoids such as dual braid monoids.

In this article, the standard correspondence between the ideal class group of a quadratic number field and the equivalence classes of binary quadratic forms of given discriminant is generalized to any base number field of narrow class…

Generalizing a theorem of Springer, we construct an extended Arason filtration by subgroups for the Witt group of quadratic forms of a general valued field, relating these subgroups with Witt-like groups of the residue field, in arbitrary…