Related papers: Structure of multicorrelation sequences with integ…

Let $E$ be an elliptic curve defined over $\mathbb{Q}$ and let $N$ be a positive integer. Now, $M_E(N)$ counts the number of primes $p$ such that the group $E_p(\mathbb{F}_p)$ is of order $N$. In an earlier joint work with Balasubramanian,…

Let $\Xi_n=\{\xi_1,\dots,\xi_n\}$ be a sample of $n$ independent points distributed in a regular closed element $K$ of the extended convex ring in $\mathbb{R}^d$ according to a probability measure $\mu$ on $K$, admitting a density function.…

We are interested in the problem of characterizing the correlations that arise when performing local measurements on separate quantum systems. In a previous work [Phys. Rev. Lett. 98, 010401 (2007)], we introduced an infinite hierarchy of…

Let G be an additive abelian group whose finite subgroups are all cyclic. Let A_1,...,A_n (n>1) be finite subsets of G with cardinality k>0, and let b_1,...,b_n be pairwise distinct elements of G with odd order. We show that for every…

Let $N_1(m)=\max\{n \colon \phi(n) \leq m\}$ and $N_1 = \{N_1(m) \colon m \in \phi(\mathbb{N})\}$ where $\phi(n)$ denotes the Euler's totient function. Masser and Shiu \cite{masser} call the elements of $N_1$ as `sparsely totient numbers'…

A classical theorem of Koksma states that for Lebesgue almost every $x>1$ the sequence $(x^n)_{n=1}^{\infty}$ is uniformly distributed modulo one. In the present paper we extend Koksma's theorem to the pair correlation setting. More…

We analyze a family of measures of general quantum correlations for composite systems, defined in terms of the bipartite entanglement necessarily created between systems and apparatuses during local measurements. For every entanglement…

We study generalized Fibonacci sequences $F_{n+1}=PF_n-QF_{n-1}$ with initial values $F_0=0$ and $F_1=1$. Let $P,Q$ be nonzero integers such that $P^2-4Q$ is not a perfect square. We show that if $Q=\pm 1$ then the sequence…

We consider polymers in which M randomly selected pairs of monomers are restricted to be in contact. Analytical arguments and numerical simulations show that an ideal (Gaussian) chain of N monomers remains expanded as long as M<<N; its mean…

We consider probability measures on the real line or unit circle with Jacobi or Verblunsky coefficients satisfying an $\ell^p$ condition and a generalized bounded variation condition. This latter condition requires that a sequence can be…

We study pointwise convergence of entangled averages of the form \[ \frac{1}{N^k}\sum_{1\leq n_1,\ldots, n_k\leq N} T_m^{n_{\alpha(m)}}A_{m-1}T^{n_{\alpha(m-1)}}_{m-1}\ldots A_2T_2^{n_{\alpha(2)}}A_1T_1^{n_{\alpha(1)}} f, \] where $f\in…

We prove nilpotency results for Lie algebras over an arbitrary field admitting a derivation, which satisfies a given polynomial identity $r(t)=0$. For the polynomial $r=t^n-1$ we obtain results on the nilpotency of Lie algebras admitting a…

We derive a tight upper bound on the probability over $\mathbf{x}=(x_1,\dots,x_\mu) \in \mathbb{Z}^\mu$ uniformly distributed in $ [0,m)^\mu$ that $f(\mathbf{x}) = 0 \bmod N$ for any $\mu$-linear polynomial $f \in…

The block entanglement entropy and fluctuations are investigated in one dimension in finite size correlated electron systems using the Gutzwiller wave function as a prototype correlated electron state. Entanglement entropy shows logarithmic…

We develop a new analytic method for quantitative mixing of automorphisms on nilmanifolds. The method is based on the introduction and solvability of \emph{multiple fractional cohomological equations of Type~$I$} (sum type). We prove that…

Motility-induced phase separation (MIPS) is a purely non-equilibrium phenomenon in which self-propelled particles phase separate without any attractive interactions. One surprising feature of MIPS is the emergence of polar, nematic, and…

We develop an extension of the process matrix (PM) framework for correlations between quantum operations with no causal order that allows multiple rounds of information exchange for each party compatibly with the assumption of well-defined…

Let $p_n$ denote the $n$-th prime number, $\{q_n\}$ be a sequence of positive numbers and $x\in\mathbb{R}$. In this note we prove that the inequality $$q_n p_{n+1}^{x}-q_{n+1}p_{n}^{x}<p_{n}^{x}p_{n+1}^{x-1}, $$ holds for infinitely many…

It is well-known that every weakly convergent sequence in $\ell_1$ is convergent in the norm topology (Schur's lemma). Phillips' lemma asserts even more strongly that if a sequence $(\mu_n)_{n\in\mathbb N}$ in $\ell_\infty'$ converges…

Integer partitions are deeply related to many phenomena in statistical physics. A question naturally arises which is of interest to physics both on "purely" theoretical and on practical, computational grounds. Is it possible to apprehend…