Related papers: Quadratic functions on torsion groups

In the present paper, new classes of wavelet functions are presented in the framework of Clifford analysis. Firstly, some classes of orthogonal polynomials are provided based on 2-parameters weight functions. Such classes englobe the well…

Let $A$ be an abelian surface over $\mathbb{Q}$ whose geometric endomorphism ring is a maximal order in a non-split quaternion algebra. Inspired by Mazur's theorem for elliptic curves, we show that the torsion subgroup of $A(\mathbb{Q})$ is…

Recently, the first-named author gave a classification of 3D consistent 6-tuples of quad-equations with the tetrahedron property; several novel asymmetric 6-tuples have been found. Due to 3D consistency, these 6-tuples can be extended to…

We define the braid groups of a two-dimensional orbifold and introduce conventions for drawing braid pictures. We use these to realize the Artin groups associated to the spherical Coxeter diagrams A_n, B_n=C_n and D_n and the affine…

We study the most elementary aspects of harmonic analysis on a homogeneous space of a deformation of the two-dimensional Euclidean group, admitting generalizations to dimensions three and four, whose quantum parameter has the physical…

Braverman and Gaitsgory gave necessary and sufficient conditions for a nonhomogeneous quadratic algebra to satisfy the Poincare-Birkhoff-Witt property when its homogeneous version is Koszul. We widen their viewpoint and consider a quotient…

For a class of closed manifolds N, we construct a family of functions on the Hamiltonian group G of the cotangent bundle T*N. These restrict to homogeneous quasi-morphisms on the subgroup generated by Hamiltonians with support in a given…

We compute the representation and class counting zeta functions for a family of torsion-free finitely generated nilpotent groups of nilpotency class $2$. These groups arise from a generalisation of one the families of unipotent groups…

A transformation is obtained which completes the unification of quadrirational Yang-Baxter maps and known integrable multi-quadratic quad equations. By combining theory from these two classes of quad-graph models we find an extension of the…

We prove several results about integral versions of Fourier duality for abelian schemes, making use of Pappas's work on integral Grothendieck-Riemann-Roch. If $S$ is smooth quasi-projective of dimension $d$ over a field and $\pi \colon X\to…

We investigate the analytic properties of a Dirichlet series involving the Fourier-Jacobi coefficients of two cusp forms for orthogonal groups of signature $(2,n+2)$. Using an orthogonal Eisenstein series of Klingen type, we obtain an…

We consider the structures formed by isogenies of abelian varieties with polarizations that are not necessarily principal, specifically with the $[\ell]$-polarizations we have previously defined. Our primary interest is in superspecial…

We give an elementary proof of the Eilenberg-Mac Lane trace isomorphism between the third 2-abelian cohomology group and quadratic forms. Our approach yields explicit constructions and we characterize when quadratic forms can be expressed…

In this paper we prove Implicit Function Theorems (IFT) for algebraic varieties defined by regular quadratic equations and, more generally, regular NTQ systems over free groups. In the model theoretic language these results state the…

In this note we consider Boolean functions defined on the discrete cube equipped with a biased product probability measure. We prove that if the spectrum of such a function is concentrated on the first two Fourier levels, then the function…

Let $\mathcal{G}=\mathrm{Spec}(A)$ be a finite and flat group scheme over the ring of algebraic integers $R$ of a number field $K$ and suppose that the generic fiber of $\mathcal{G}$ is the constant group scheme over $K$ for a finite group…

We consider arbitrary algebraic families of lower order deformations of nondegenerate toric exponential sums over a finite field. We construct a relative polytope with the aid of which we define a ring of coefficients consisting of p-adic…

A definition is offered of the factorial characters of the general linear group, the symplectic group and the orthogonal group in an odd dimensional space. It is shown that these characters satisfy certain flagged Jacobi-Trudi identities.…

Let q be an integral quadratic form of signature (2,m+2). We will show that the Siegel theta functions attached to q satisfies certain symmetries. As an application, we prove the symmetries for automorphic forms on the orthogonal group of q…

Non-perturbative partition functions of quantum theories constitute a class of $\tau-$functions, which are distinguished satisfying Hirota's bilinear identities(BI). To make this statement general, there must be a proper definition of…