Related papers: Quadratic functions on torsion groups

In this paper, we introduce a new class of $\ell$-adic sheaves, which we call quadratic $\ell$-adic sheaves, on connected unipotent commutative algebraic groups over finite fields. They are sheaf-theoretic enhancements of quadratic forms on…

We address the problem of which functions can arise as Dehn functions of K\"ahler groups. We explain why there are examples of K\"ahler groups with linear, quadratic, and exponential Dehn function. We then proceed to show that there is an…

We provide an algorithm to compute generators of the orthogonal group of the discriminant group associated to an integral quadratic lattice over the integers. We give a closed formula for its order.

We prove that the Dehn function of a group of Stallings that is finitely presented but not of type F_3 is quadratic. To appear in Geometric and Functional Analysis.

From the structure of the category of representations of an affine cycle-free quiver, we determine an explicit linear form on the space of regular cuspidal functions over a finite field: its kernel is exactly the space of cuspidal…

It is well known that over an infinite field the ring of symmetric functions in a finite number of variables is isomorphic to the one of polynomial functions on matrices that are invariants by the action of conjugation by general linear…

Riemannian Geometry, Topology and Dynamics permit to introduce partially defined holomorphic functions on the variety of representations of the fundamental group of a manifold. The functions we consider are the complex valued Ray-Singer…

We present a new systematic method to construct Abelian functions on Jacobian varieties of plane, algebraic curves. The main tool used is a symmetric generalisation of the bilinear operator defined in the work of Baker and Hirota. We give…

Quadrature formulas for spheres, the rotation group, and other compact, homogeneous manifolds are important in a number of applications and have been the subject of recent research. The main purpose of this paper is to study coordinate…

We introduce affine Stanley symmetric functions for the special orthogonal groups, a class of symmetric functions that model the cohomology of the affine Grassmannian, continuing the work of Lam and Lam, Schilling, and Shimozono on the…

Weyl-orbit functions have been defined for each simple Lie algebra, and permit Fourier-like analysis on the fundamental region of the corresponding affine Weyl group. They have also been discretized, using a refinement of the coweight…

Isotropic functions of positions $\hat{\bf r}_1, \hat{\bf r}_2,\ldots, \hat{\bf r}_N$, i.e. functions invariant under simultaneous rotations of all the coordinates, are conveniently formed using spherical harmonics and Clebsch-Gordan…

We prove the equivalence of two conjectural constructions of unramified cuspidal automorphic functions on the adelic group GL_n(A) associated to an irreducible l-adic local system of rank n on an algebraic curve X over a finite field. The…

Generalisations of the bent property of a boolean function are presented, by proposing spectral analysis with respect to a well-chosen set of local unitary transforms. Quadratic boolean functions are related to simple graphs and it is shown…

The Walsh transform $\widehat{Q}$ of a quadratic function $Q:F_{p^n}\rightarrow F_p$ satisfies $|\widehat{Q}(b)| \in \{0,p^{\frac{n+s}{2}}\}$ for all $b\in F_{p^n}$, where $0\le s\le n-1$ is an integer depending on $Q$. In this article, we…

Four families of special functions, depending on n variables, are studied. We call them symmetric and antisymmetric multivariate sine and cosine functions. They are given as determinants or antideterminants of matrices, whose matrix…

A linear algebraic group $G$ is represented by the linear space of its algebraic functions $F(G)$ endowed with multiplication and comultiplication which turn it into a Hopf algebra. Supplying $G$ with a Poisson structure, we get a quantized…

Let $(0, a_1, \ldots, a_{d-1})_n$ denote the function $f_n(x_0, x_1, \ldots, x_{n-1})$ of degree $d$ in $n$ variables generated by the monomial $x_0x_{a_1} \cdots x_{a_{d-1}}$ and having the property that $f_n$ is invariant under cyclic…

We prove various results connecting structural or algebraic properties of graphs and groups to conditions on their spaces of harmonic functions. In particular: we show that a group with a finitely supported symmetric measure has a…

We consider classes $ \mathcal{A}_M(S) $ of functions holomorphic in an open plane sector $ S $ and belonging to a strongly non-quasianalytic class on the closure of $ S $. In $ \mathcal{A}_M(S) $, we construct functions which are flat at…