Related papers: Factorizations of Characteristic Functions

A simple definition of torsion theory is presented, as a factorization system with both classes satisfying the 3--for--2 property. Comparisons with the traditional notion are given, as well as connections with the notions of fibration and…

A number of mathematical methods have been shown to model the zeroes of $L$-functions with remarkable success, including the Ratios Conjecture and Random Matrix Theory. In order to understand the structure of convolutions of families of…

In this paper, we obtain some characterizations of the (strong) Birkhoff--James orthogonality for elements of Hilbert $C^*$-modules and certain elements of $\mathbb{B}(\mathscr{H})$. Moreover, we obtain a kind of Pythagorean relation for…

Functions of bounded characteristic in simply connected domains have a classical factorization to Blaschke, outer and singular inner parts. The latter has a singular measure on the boundary assigned to it. The exponential speed of change of…

Let $K$ be a quadratic field, and let $\zeta_K$ its Dedekind zeta function. In this paper we introduce a factorization of $\zeta_K$ into two functions, $L_1$ and $L_2$, defined as partial Euler products of $\zeta_K$, which lead to a…

Theorem 1.2.6 of [ATW20] provides a relatively functorial logarithmic principalization of ideals on relative logarithmic orbifolds $X\to B$ in characteristic 0, relying on a delicate monomialization theorem for Kummer ideals. The paper…

Character tables of finite groups and closely related commutative algebras have been investigated recently using new perspectives arising from the AdS/CFT correspondence and low-dimensional topological quantum field theories. Two important…

The aim of the paper is twofold. Firstly, we give an axiomatic presentation of Donaldson-Thomas theory for categories of homological dimension at most one with potential. In particular, we provide rigorous proofs of all standard results…

Given a generically \'etale morphism $f\colon Y\to X$ of quasi-smooth Berkovich curves, we define a different function $\delta_f\colon Y\to[0,1]$ that measures the wildness of the topological ramification locus of $f$. This provides a new…

$W$-representation realizes partition functions by an action of a cut-and-join-like operator on the vacuum state with a zero-mode background. We provide explicit formulas of this kind for $\beta$- and $q,t$-deformations of the simplest…

We give a proof of the existence of Asai, exterior square, and symmetric square local $L$-functions, $\gamma$-factors and root numbers in characteristic $p$, including the case of $p = 2$. Our study is made possible by developing the…

A pair of commuting Hilbert space contractions $(T_1,T_2)$ is said to be toral if there is a polynomial $p \in \mathbb C[z_1,z_2]$ such that its zero set $Z(p)$ defines a distinguished variety in the bidisc $\mathbb D^2$ and $p(T_1,T_2)=0$.…

We prove two conjectures regarding the representation growth of groups of type $A_2$. The first, conjectured by Avni, Klopsch, Onn and Voll, regards the uniformity of representation zeta functions over local complete discrete valuation…

For any bounded domain $\Omega$ in $\mathbb C^m,$ let ${\mathrm B}_1(\Omega)$ denote the Cowen-Douglas class of commuting $m$-tuples of bounded linear operators. For an $m$-tuple $\boldsymbol T$ in the Cowen-Douglas class ${\mathrm…

In further study of the application of crossed-product functors to the Baum-Connes Conjecture, Buss, Echterhoff, and Willett introduced various other properties that crossed-product functors may have. Here we introduce and study analogues…

The results for structure function $F_L$, obtained in the $k_T$-factorization and collinear approaches, are compared with recent H1 experimental data at fixed $W$ values.

Using the method of Tracy and Widom we rederive the correlation functions for \beta=1 Hermitian and real asymmetric ensembles of N x N matrices with N odd.

We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U(N), O(2N) and USp(2N). In each case the result can be expressed in…

Let $H_m(\mathbb B)$ be the analytic functional Hilbert space on the unit ball $\mathbb B \subset \mathbb C^n$ with reproducing kernel $K_m(z,w) = (1 - \langle z,w \rangle)^{-m}$. Using algebraic operator identities we characterize those…

In this investigation of character tables of finite groups we study basic sets and associated representation theoretic data for complementary sets of conjugacy classes. For the symmetric groups we find unexpected properties of characters on…