Related papers: The shape of cubic fields
A system of generalized coherent states for the de Sitter group obeying Klein-Gordon equation and corresponding to the massive spin zero particles over the de Sitter space is considered. This allows us to construct the quantized scalar…
We study singularities of surfaces which are given by Kenmotsu-type formula with prescribed unbounded mean curvature.
A simple, new method for solving for the $Q^2$ evolution of parton distributions in perturbative QCD using cubic splines is described and applied to the evolution of nonsinglet quark distributions.
We describe a new viewpoint on canonical quantization of linear fields on a general curved background that encompasses and generalizes the standard treatment of canonical QFT given in textbooks. Our method permits the construction of pure…
This article shows how to find the solution of an arbitrary quintic equation by performing two simultaneous folds on a sheet of paper. The folds achieve specific incidences between a set of points and lines that are determined by the…
A general scheme for determining and studying hydrodynamic type systems describing integrable deformations of algebraic curves is applied to cubic curves. Lagrange resolvents of the theory of cubic equations are used to derive and…
We construct a bosonic quantum field on a general quantum graph. Consistency of the construction leads to the calculation of the total scattering matrix of the graph. This matrix is equivalent to the one already proposed using generalized…
Since the study by Jacobi and Hecke, Hecke-type series have received a lot of attention. Unlike such series associated with indefinite quadratic forms, identities on Hecke-type series associated with definite quadratic forms are quite rare…
A quasi-order is a binary, reflexive and transitive relation. In the Journal of Pure and Applied Algebra 45 (1987), S.M. Fakhruddin introduced the notion of (totally) quasi-ordered fields and showed that each such field is either an ordered…
We investigate the existence of coordinate transformations which bring a given vector field on a manifold equipped with an involutive distribution into the form of a second-order differential equation field with parameters. We define…
We present computational results on the divisor class number and the regulator of a cubic function field over a large base field. The underlying method is based on approximations of the Euler product representation of the zeta function of…
We investigate bosonic fields possessing two mass and spin states. The density matrix in the first order formalism is obtained. The quantization of fields in the first order formulation is performed and propagators are found.
We show that infinitely many cubic fields have class group of 2-rank 1.
We study domination of quadratic forms in the abstract setting of ordered Hilbert spaces. Our main result gives a characterization in terms of the associated forms. This generalizes and unifies various earlier works. Along the way we…
In 1951, Ankeny, Artin, and Chowla published a brief note containing four congruence relations involving the class number of $\mathbb{Q}(\sqrt{d})$ for positive squarefree integers $d\equiv 1 \bmod{4}$. Many of the ideas present in their…
In 1981, Uchida proved a conditional version of the Hom-form of the Grothendieck birational anabelian conjecture for number fields. In this paper we prove an m-step solvable conditional version of the Grothendieck birational anabelian…
We use the method of Bruinier--Raum to show that symmetric formal Fourier--Jacobi series, in the cases of norm-Euclidean imaginary quadratic fields, are Hermitian modular forms. Consequently, combining a theorem of Yifeng Liu, we deduce…
We extend field patching to the setting of Berkovich analytic geometry and use it to prove a local-global principle over function fields of analytic curves. We apply this result to quadratic forms, and combine it with sufficient conditions…
Classes of pairs of ternary quadratic forms parametrize quartic rings by a result of Bhargava. We give an algorithm for finding a pair of ternary quadratic forms that parametrize a given order of a quartic field. We examine a new technique,…
A Chebyshev-type quadrature for a given weight function is a quadrature formula with equal weights. In this work we show that a method presented by Kane may be used to produce tight bounds for the minimal number of nodes required in…