Related papers: Products of Factorials Modulo p

We consider a problem of P. Erdos, A. M. Odlyzko and A. Sarkozy about the representation of residue classes modulo m by products of two not too large primes. While it seems that even the Extended Riemann Hypothesis is not powerful enough to…

Certain new inequalities for the sums of factorials are presented.

We consider the moments of products of complete elliptic integrals of the first and second kinds. In particular, we derive new results using elementary means, aided by computer experimentation and a theorem of W. Zudilin. Diverse related…

We study the class of those linear relations that can be factorized as products of idempotent relations. We provide several characterizations of this class, extending known factorization results for operators to the more general setting of…

We state a conjecture on the reduction modulo the defining characteristic of a unipotent representation of a finite reductive group.

We give a new expression for the number of factorizations of a full cycle into an ordered product of permutations of specified cycle types. This is done through purely algebraic means, extending work of Biane. We deduce from our result a…

We study characteristic polynomials of symmetric matrices with entries ${i+j\choose i}$ the binomial coefficients, over finite fields.

We study finite dimensional representations of the projective modular group. Various explicit dimension formulas are given.

We give a factorization of the cycle of a bounded complex of vector bundles in terms of certain associated differential forms and residue currents. This is a generalization of previous results in the case when the complex is a locally free…

The aim of this paper is to introduce and study a large class of $\mathfrak{g}$-module algebras which we call factorizable by generalizing the Gauss factorization of (square or rectangular) matrices. This class includes coordinate algebras…

We present new and streamlined proofs of various formulae for products and ratios of characteristic polynomials of random Hermitian matrices that have appeared recently in the literature.

In this paper we discuss the relationship between direct products of monounary algebras and their components, with respect to the properties of residual finiteness, strong/weak subalgebra separability, and complete separability. For each of…

We prove that the sequence $n!\,(\bmod\,p)$ occupies at least $\sqrt{\frac{3}{2}N}$ residue classes in the short interval $H\le n \le H+N$ and $N\gg p^{\frac{1}{4}}$ improving previously known trivial bound $\sqrt{N}.$ In the other…

It is investigated how graded variants of integral and complete integral closures behave under coarsening functors and under formation of group algebras.

The tensor product of $L$ copies of a single vector, such as $p_{i_1} ... p_{i_L}$, can be analyzed in terms of angular momentum. When $p_{i_1} ... p_{i_L}$ is decomposed into a sum of components $( p_{i_1} ... p_{i_L} )^L_\ell$, each…

We study arithmetic properties of factorizations of elements into products of generators, in monoids given with explicit presentations. After relating and comparing this perspective to the more usual approach of factoring into products of…

We study primary submodules and primary decompositions from a differential and computational point of view. Our main theoretical contribution is a general structure theory and a representation theorem for primary submodules of an arbitrary…

Which matrices can be written as sums or products of square-zero matrices? This question is the central premise of this dissertation. Over the past 25 years a significant body of research on products and linear combinations of square-zero…

It is shown that the idempotent completion of the additive hull of the tensor product of the residue category of the category of paths of a locally finite quiver modulo an admissible ideal and a dualizing category is dualizing. Furthermore,…

We study the moduli space of a product of stable varieties over the field of complex numbers, as defined via the minimal model program. Our main results are: (a) taking products gives a well-defined morphism from the product of moduli…