Related papers: Determining universality of $m$-gonal form with fi…

Unitary representations of the fundamental group of a Kahler manifold correspond to polystable vector bundles (with vanishing Chern classes). Semisimple linear representations correspond to polystable Higgs bundles. In this paper we find…

Perfect quadratic forms give a toroidal compactification of the moduli space of principally polarized abelian g-folds that is Q-factorial and whose ample classes are characterized, over any base. In characteristic zero it has canonical…

We consider polynomials $Q:=\sum _{j=0}^da_jx^j$, $a_j\in \mathbb{R}^*$, with all roots real. When the {\em sign pattern} $\sigma (Q):=({\rm sgn}(a_d),{\rm sgn}(a_{d-1})$, $\ldots$, ${\rm sgn}(a_0))$ has $\tilde{c}$ sign changes, the…

We give an explicit description of the coefficients of the formal power series (1-x)(1-x^2)(1-x^3)(1-x^5)(1-x^8)(1-x^13)... In particular, we show that all the coefficients are equal to -1, 0 or 1.

A new Dimensional Regularization of $\gamma_5$ is proposed. Cyclicity and Lorentz covariance are enforced. The extension to generic dimension is based on the integral representation of the trace of gamma's, presented in a previous paper.

Let $\pi$ be an irreducible unitary cuspidal representation of $GL_m({\Bbb A}_{\Bbb Q})$ and $L(s,\,\pi)$ be the global $L-$function attached to $\pi$. If ${\rm Re}(s)>1$, $L(s,\,\pi)$ has a Dirichlet series expression. When $\pi$ is…

Antimonotonous quadratic forms generalizing P-faithful posets defined by authors earlier are introduced. The criterion of antimonotonousness is given for posets with positive semidefinite quadratic forms. As consequence the new proofs of…

We determine, up to the equivalence of first-order interdefinability, all structures which are first-order definable in the random partial order. It turns out that these structures fall into precisely five equivalence classes. We achieve…

This note presents some properties of the variety of planes $F_2(X)\subset G(3,7)$ of a cubic $5$-fold $X\subset \mathbb P^6$. A cotangent bundle exact sequence is first derived from the remark made by Iliev and Manivel that $F_2(X)$ sits…

Two geodesically (projectively) equivalent Finsler metrics determine a set of invariant volume forms on the projective sphere bundle. Their proportionality factors are geodesically invariant functions and hence they are first integrals.…

We will introduce formal frames of manifolds, which are a generalization of ordinary frames. Their fundamental properties are discussed. In particular, canonical forms are introduced, and torsions are defined in terms of them as a…

By polynomial (or extended binomial) coefficients, we mean the coefficients in the expansion of integral powers, positive and negative, of the polynomial $1+t +\cdots +t^{m}$; $m\geq 1$ being a fixed integer. We will establish several…

In this paper, we give a general formula to determine the quantization coefficients for uniform distributions defined on the boundaries of different regular $m$-sided polygons inscribed in a circle. The result shows that the quantization…

Let $G=Sp(4,\mathbb{R})$ and let $\pi$ be an irreducible, unitary representation of $G$ which is cohomological with respect to trivial coefficients. Using the inclusion from $SO(5,\mathbb{C})$ to $GL(5,\mathbb{C})$, we transfer $\pi$ to an…

We prove new upper bounds on the number of representations of rational numbers $\frac{m}{n}$ as a sum of $4$ unit fractions, giving five different regions, depending on the size of $m$ in terms of $n$. In particular, we improve the most…

Vogel's universality implies a unified description of the adjoint sector of representation theory for simple Lie algebras in terms of three parameters $\alpha,\beta,\gamma$, which are homogeneous coordinates of Vogel's plane. Actually this…

A (positive definite integral) quadratic form is called almost 2-universal if it represents all (positive definite integral) binary quadratic forms except those in only finitely many equivalence classes. Oh [7] determined all almost…

The characteristic forms in the bundle of connections of a principal bundle P over M determine the characteristic classes of P for degree less or equal to the dimension of M, and differential forms on the space of connections for higher…

A one to one correspondence between regular generalized bent functions from $\F_2^n$ to $\Z_{2^m},$ and $m-$tuples of Boolean bent functions is established. This correspondence maps self-dual (resp. anti-self-dual) generalized bent…

Let $\pi$ be an irreducible unitary cuspidal representation for $GL_m({\Bbb A}_{\Bbb Q})$, and let $L(s, \pi)$ be the automorphic $L$-function attached to $\pi$, which has a Dirichlet series expression in the half-plane $\mbox{Re} s>1$.…