相关论文: Polynomial central set theorem near zero

We display a new family of prime ideals with unbounded minimal number of generators in a three-dimensional power series ring over a field of characteristic zero. These primes are obtained as the kernel of a quasi-monomial algebra…

We provide upper bounds on the largest subsets of $\{1,2,\dots,N\}$ with no differences of the form $h_1(n_1)+\cdots+h_{\ell}(n_{\ell})$ with $n_i\in \mathbb{N}$ or $h_1(p_1)+\cdots+h_{\ell}(p_{\ell})$ with $p_i$ prime, where $h_i\in…

The classical Hermite-Biehler theorem describes possible zero sets of complex linear combinations of two real polynomials whose zeros strictly interlace. We provide the full characterization of zero sets for the case when this interlacing…

The first part of this paper complements previous results on characterization of polynomials of least deviation from zero in Sobolev $p$-norm ($1<p<\infty$) for the case $p=1$. Some relevant examples are indicated. The second part deals…

The study of the size of subsets in a semigroup have shown that many of these subsets have strong combinatorial properties and contribute richly to the algebraic structure of the Stone-Cech compactification of a discrete semigroup. N.…

In \cite[Proposition 8.21 Page-169]{F} Using the methods of topological dynamics, H. Furstenberg introduced the notion of central set and proved the famous Central Sets Theorem. Later, in \cite{DHS}, D. De, H. Hindman and D. Struss…

Following an approach presented by N. Frantzikinakis, B. Host and B. Kra, we show that the parameters in the multidimensional Szemer\'edi theorem for closest integer polynomials have non-empty intersection with the set of shifted primes…

The theorem of Shannon-McMillan-Breiman states that for every generating partition on an ergodic system, the exponential decay rate of the measure of cylinder sets equals the metric entropy almost everywhere (provided the entropy is…

For random systems of $K$ polynomials in $N + 1$ real variables which include the models of Kostlan (1987) and Shub and Smale (1993), we prove that the number of zeros on the unit sphere for $K = N$ or the Hausdorff measure of the zero set…

It is known that there are many notions of largeness in a semigroup that own rich combinatorial properties. In this paper, we focus on partition and almost disjoint properties of these notions. One of the most remarkable results with…

Interpolation theory for complex polynomials is well understood. In the non-commutative quaternionic setting, the polynomials can be evaluated "on the left" and "on the right". If the interpolation problem involves interpolation conditions…

We prove an almost sure central limit theorem on the Poisson space, which is perfectly tailored for stabilizing functionals emerging in stochastic geometry. As a consequence, we provide almost sure central limit theorems for $(i)$ the total…

This paper deals with the numerical approximation of normalizing constants produced by particle methods, in the general framework of Feynman-Kac sequences of measures. It is well-known that the corresponding estimates satisfy a central…

We generalise a necessary and sufficient condition given by Cohn for all the zeros of a self-inversive polynomial to be on the unit circle. Our theorem implies some sufficient conditions found by Lakatos, Losonczi and Schinzel. We apply our…

In [1] the authors showed some basic properties of a pre-order that arose in combinatorial number theory, namely the finite embeddability between sets of natural numbers, and they presented its generalization to ultrafilters, which is…

In a recent paper by Harada, Seceleanu, and \c{S}ega, the Hilbert function, betti table, and graded minimal free resolution of a general principal symmetric ideal are determined when the number of variables in the polynomial ring is…

The Skolem Problem asks to determine whether a given integer linear recurrence sequence has a zero term. This problem arises across a wide range of topics in computer science, including loop termination, formal languages, automata theory,…

We define the local empirical process, based on $n$ i.i.d. random vectors in dimension $d$, in the neighborhood of the boundary of a fixed set. Under natural conditions on the shrinking neighborhood, we show that, for these local empirical…

Hindman's theorem and van der Waerden's theorem are two classical Ramsey theoretic results, the first one deals with finite configurations and the second one deals with infinite configurations. The Central Sets Theorem due to Furstenberg is…

Given an $n*n$ sparse symmetric matrix with $m$ nonzero entries, performing Gaussian elimination may turn some zeroes into nonzero values. To maintain the matrix sparse, we would like to minimize the number $k$ of these changes, hence…