相关论文: Average Representation Numbers For Spinor Genera

Based on BONGs theory, we prove the norm principle for integral and relative integral spinor norms of quadratic forms over general dyadic local fields, respectively. By virtue of these results, we further establish the arithmetic version of…

We present an inductive method for constructing the basic spin representations of the double covers of the symmetric groups over fields of any characteristic.

In this paper we use the theory of modular forms to find formulas for the number of representations of a positive integer by certain class of quadratic forms in eight variables, viz., forms of the form $a_1x_1^2 + a_2 x_2^2 + a_3 x_3^2 +…

In this paper, we consider representations of integers as sums of at most four distinct $m$-gonal numbers (allowing a fixed number of repeats of each polygonal number occurring in the sum). We show that the number of such representations…

Given a real representation of the Clifford algebra corresponding to $R^{p+q}$ with metric of signature $(p,q)$, we demonstrate the existence of two natural bilinear forms on the space of spinors. With the Clifford action of $k$-forms on…

We give an asymptotic for the number of prime solutions to $Q(x_1,\dots, x_8) = N$, subject to a mild non-degeneracy condition on the homogeneous quadratic form $Q$. The argument initially proceeds via the circle method, but this does not…

We prove a quantitative version of Oppenheim's conjecture for generic ternary indefinite quadratic forms. Our results are inspired by and analogous to recent results for diagonal quadratic forms due to Bourgain.

Let $Q$ be a positive-definite quaternary quadratic form with prime discriminant. We give an explicit lower bound on the number of representations of a positive integer $n$ by $Q$. This problem is connected with deriving an upper bound on…

In this article, we give all the Weitzenb\"ock-type formulas among the geometric first order differential operators on the spinor fields with spin $j+1/2$ over Riemannian spin manifolds of constant curvature. Then we find an explicit…

For two positive definite integral ternary quadratic forms $f$ and $g$ and a positive integer $n$, if $n\cdot g$ is represented by $f$ and $n\cdot dg=df$, then the pair $(f,g)$ is called a representable pair by scaling $n$. The set of all…

The spinor representation is developed and used to investigate minimal surfaces in ${\bfR}^3$ with embedded planar ends. The moduli spaces of planar-ended minimal spheres and real projective planes are determined, and new families of…

If H and D are two orders in a central simple algebra A with D of maximal rank and containing H, the theory of representation fields describes the set of spinor genera of orders in the genus of D representing the order H. When H is…

We provide an alternative formula for spin distributions of generic p-spin glass models. As a main application of this expression, we write spin statistics as solutions of partial differential equations and we show that the generic p-spin…

The aim of this paper is to represent any polynomial in terms of the degenerate Frobenius-Euler polynomials and more generally of the higher-order degenerate Frobenius-Euler polynomials. We derive explicit formulas with the help of umbral…

A collective field method is extended to obtain all the explicit solutions of the generalized Calogero-Sutherland models that are characterized by the roots of all the classical groups, including the solutions corresponding to spinor…

We generalize the concept of cubic group into any dimension and derive their conjugate classifications and representation theorys. Double group and spinor representation are defined. A detailed calculation is carried out on the structures…

It is known that a presentation of the knot group of a branched twist spin is obtained from a Wirtinger presentation of the original 1-knot group by adding a generator corresponding to a regular orbit of the circle action and a certain…

It is a commonplace that any theory can be written in any coordinates via tensor calculus. But it is claimed that spinors as such cannot be represented in coordinates in a curved space-time. What general covariance means for theories with…

In the present article, real number representations, that are generalizations of classical positive and alternating representations of numbers, are introduced and investigated. The main metric relation, properties of cylinder sets are…

H. J. S. Smith proved Fermat's two-square theorem using the notion of palindromic continuants. In this paper we extend Smith's approach to proper binary quadratic form representations in some commutative Euclidean rings, including rings of…