Related papers: Multiplicative complements I

In this paper we prove some results on the possible multiplicative orders of $\alpha + \alpha^{-1}$ when $\alpha$ is a non-zero element of a finite field of characteristic 2. The results of the paper rely on a previous investigation on the…

We propose the extension of the complex numbers to be the new domain where new concepts, like negative and imaginary probabilities, can be defined. The unit of the new space is defined as the solution of the unsolvable equation in the…

The Multiplicity conjecture of Herzog, Huneke, and Srinivasan states an upper bound for the multiplicity of any graded $k$-algebra as well as a lower bound for Cohen-Macaulay algebras. In this note we extend this conjecture in several…

In this paper, we study the distribution of difference of multiplicative and additive characters modulo $p$ at consecutive polynomial values. More precisely, for an interval $I$ over finite field and $0<m<1$, we investigate the following…

By using a selective filtration argument, we prove that the satisfiability problem of the unimodal logic of density is in $EXPTIME$. By using a tableau-like approach, we prove that the satisfiability problem of the bimodal logic of weak…

We show that the biharmonic Hilbert complex with mixed boundary conditions on bounded strong Lipschitz domains is closed and compact. The crucial results are compact embeddings which follow by abstract arguments using functional analysis…

We consider a problem of bounding the maximal possible multiplicity of a zero at of some expansions $\sum a_i F_i(x)$, at a certain point $c,$ depending on the chosen family $\{F_i \}$. The most important example is a polynomial with $c=1.$…

In this paper, we study a density version of Waring's problem. We prove that a positive density subset of $k$th-powers forms an asymptotic additive basis of order $O(k^2)$ provided that the relative lower density of the set is greater than…

We explore the distribution of class numbers $h(d)$ of indefinite binary quadratic forms, for discriminants $d$ such that the corresponding fundamental unit $\varepsilon_d$ is lower than $d^{1/2+\alpha}$, where $0<\alpha<1/2$. To do so we…

The set A = {a_n} of nonnegative integers is an asymptotic basis of order h if every sufficiently large integer can be represented as the sum of h elements of A. If a_n ~ alpha n^h for some real number alpha > 0, then alpha is called an…

In part I of this paper we studied additive decomposability of the set $\F_y$ of th $y$-smooth numbers and the multiplicative decomposability of the shifted set $\g_y=\F_y+\{1\}$. In this paper, focusing on the case of 'large' functions…

Inspired by the chemical metaphor, this paper proposes an extension of Linda-like languages in the aim of modeling the coordination of complex distributed systems. The new language manipulates finite sets of tuples and distributes a density…

We derive quantitative continuity estimates for the higher-order derivatives of the integrated density of states (IDS) with respect to the disorder parameter for the Anderson model on $\ell^2(\mathbb{G})$. Here $\mathbb{G}=\mathbb{Z}^d$ or…

Cobham's theorem asserts that if a sequence is automatic with respect to two multiplicatively independent bases, then it is ultimately periodic. We prove a stronger density version of the result: if two sequences which are automatic with…

Given a countable set X (usually taken to be N or Z), an infinite permutation $\pi$ of X is a linear ordering $<_\pi$ of X. This paper investigates the combinatorial complexity of infinite permutations on N associated with the image of…

We construct a homogeneous subspace of $2^\omega$ whose complement is dense in $2^\omega$ and rigid. Using the same method, assuming Martin's Axiom, we also construct a countable dense homogeneous subspace of $2^\omega$ whose complement is…

We prove that the integral points are potentially Zariski dense in the complement of a reduced effective singular anticanonical divisor in a smooth del Pezzo surface, with the exception of $\mathbb{P}^2$ minus three concurrent lines (for…

For any infinite zero-density integer set M, we found a rigid measure-preserving transformation mixing along M by answering Bergelson's question. Gaussian and Poisson suspensions over infinite constructions are suggested as suitable…

We provide a multidimensional extension of previous results on the existence of polynomial progressions in dense subsets of the primes. Let $A$ be a subset of the prime lattice - the d-fold direct product of the primes - of positive…

This work is a study of polynomial compositions having a fixed number of terms. We outline a recursive method to describe these characterizations, give some particular results and discuss the general case. In the final sections, some…