Related papers: MMH* with arbitrary modulus is always almost-unive…

We investigate the spectral properties of the product of $M$ complex non-Hermitian random matrices that are obtained by removing $L$ rows and columns of larger unitary random matrices uniformly distributed on the group ${\rm U}(N+L)$. Such…

Primordial black holes (PBHs) are expected to accrete particle dark matter around them to form ultracompact minihalos (UCMHs), if the PBHs themselves are not most of the dark matter. We show that if most dark matter is a thermal relic, then…

We propose the segmented iHMM (siHMM), a hierarchical infinite hidden Markov model (iHMM) that supports a simple, efficient inference scheme. The siHMM is well suited to segmentation problems, where the goal is to identify points at which a…

Let $ \Omega \subset \mathbb{C}^m $ be an open, connected and bounded set and $\mathcal{A}(\Omega)$ be a function algebra of holomorphic functions on $\Omega$. Suppose that $\mathcal{M}_q$ is the quotient Hilbert module obtained from a…

Let $\{x_{\alpha}\}_{\alpha \in \mathbb{Z}}$ and $\{y_{\alpha}\}_{\alpha \in \mathbb{Z}}$ be two independent collections of zero mean, unit variance random variables with uniformly bounded moments of all orders. Consider a nonsymmetric…

In many simple integral domains, such as $\mathbb{Z}$ or $\mathbb{Z}[i]$, there is a straightforward procedure to determine if an element is prime by simply reducing to a direct check of finitely many potential divisors. Despite the fact…

The structure of the multiplicative group $M_n = ({\mathbb Z}/n{\mathbb Z})^\times$ encodes a great deal of arithmetic information about the integer $n$ (examples include $\phi(n)$, the Carmichael function $\lambda(n)$, and the number…

We find a nontrivial upper bound on the average value of the function M(n) which associates to every positive integer n the minimal Hamming weight of a multiple of n. Some new results about the equation M(n)=M(n') are given.

We introduce, motivate and study $\varepsilon$-almost collision-flat (ACFU) universal hash functions $f:\mathcal X\times\mathcal S\to\mathcal A$. Their main property is that the number of collisions in any given value is bounded. Each…

About a century ago, P. A. MacMahon introduced a class of $q$-series, which are nowadays referred to as MacMahon series. More recently, in 2013, G. E. Andrews and S. C. F. Rose revealed the quasimodular property of these series. In this…

For each positive integer $n$, we denote by $\omega^*(n)$ the number of shifted-prime divisors $p-1$ of $n$, i.e., \[\omega^*(n):=\sum_{p-1\mid n}1.\] First introduced by Prachar in 1955, this function has interesting applications in…

The general applicability and ease of use of the pseudo-marginal Metropolis--Hastings (PMMH) algorithm, and particle Metropolis--Hastings in particular, makes it a popular method for inference on discretely observed Markovian stochastic…

A C*-algebra (or a group) is called MF (matricial field) if it admits finite dimensional approximate unitary representations which are approximately injective, where approximately is meant with respect to the operator norm. It is proved…

We define possibly unsaturated, upper semicontinuous Fell bundles over Hausdorff, locally compact groupoids and establish a universal property for representations of their full section C*-algebras on Hilbert modules over arbitrary…

It is observed that the infinite matrix with entries $(\sqrt{mn}\log (mn))^{-1}$ for $m, n\ge 2$ appears as the matrix of the integral operator $\mathbf{H}f(s):=\int_{1/2}^{+\infty}f(w)(\zeta(w+s)-1)dw$ with respect to the basis…

In 2007, G.E. Andrews introduced the $(n+1)$-variable combinatorial generating function $R_n(x_1,x_2,\cdots,x_n;q)$ for ranks of $n$-marked Durfee symbols, an $(n+1)$-dimensional multisum, as a vast generalization to the ordinary…

The modular case of the Andr\'e-Oort Conjecture is a theorem of Andre and Pila, having at its heart the well-known modular function j. I give an overview of two other `nonclassical' classes of modular function, namely the quasimodular (QM)…

Let $q$ be a prime power, $G=GL_n(q)$ and let $U\leqslant G$ be the subgroup of (lower) unitriangular matrices in $G$. For a partition $\lambda$ of $n$ denote the corresponding unipotent Specht module over the complex field $\C$ for $G$ by…

Generalized Cunningham chains are sets of the form $\{f^n(z)\}_{n\ge0}$ where all its elements are prime numbers and $f$ is a linear polynomial with integer coefficients. We generalize this definition further to include starting terms that…

Projective Reed-Muller codes correspond to subcodes of the Reed-Muller code in which the polynomials being evaluated to yield codewords, are restricted to be homogeneous. The Generalized Hamming Weights (GHW) of a code ${\cal C}$, identify…