Related papers: Fattening up Warning's Second Theorem

We present a restricted variable generalization of Warning's Second Theorem (a result giving a lower bound on the number of solutions of a low degree polynomial system over a finite field, assuming one solution exists). This is analogous to…

We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.

In this paper we obtain sharp results for Waring's problem over general finite rings, by using a combination of Artin-Wedderburn theory and Hensel's lemma and building on new proofs of analogous results over finite fields that are achieved…

We give conditions under which the number of solutions of a system of polynomial equations over a finite field F_q of characteristic p is divisible by p. Our setup involves the substitution t_i |-> f_i(t_i) for auxiliary polynomials…

In this paper we give a factorization theorem for the ring of exponential polynomials in many variables over an algebraically closed field of characteristic 0 with an exponentiation. This is a generalization of the factorization theorem due…

Associated to each random variable $Y$ having a finite moment generating function, we introduce a different generalization of the Stirling numbers of the second kind. Some characterizations and specific examples of such generalized numbers…

We present generalisations of Wilson's theorem for double factorials, hyperfactorials, subfactorials and superfactorials.

We prove measurable analogues of Whitney's classical theorems on weak isomorphisms of finite graphs. In the setting of locally finite graphings, we introduce a notion of weak isomorphism as an edge-measure-preserving Borel bijection that…

We pursue various restricted variable generalizations of the Chevalley-Warning theorem for low degree polynomial systems over a finite field. Our first such result involves variables restricted to Cartesian products of the Vandermonde…

We study the local limit theorem for weighted sums of Bernoulli variables. We show on examples that this is an important question in the general theory of the local limit theorem, and which turns up to be not well explored. The examples we…

We prove several bounds on the number of incidences between two sets of multivariate polynomials of bounded degree over finite fields. From these results, we deduce bounds on incidences between points and multivariate polynomials, extending…

This article provides a gentle introduction for a general mathematical audience to the factorization theory of motion polynomials and its application in mechanism science. This theory connects in a rather unexpected way a seemingly abstract…

We prove a general duality theorem for tangle-like dense objects in combinatorial structures such as graphs and matroids. This paper continues, and assumes familiarity with, the theory developed in [6]

In this note, we use the concept of a polynomial ring to give an elementary proof to Cayley-Hamilton Theorem. We also give an elementary proof to Birkhoff theorem on Bi-stochastic matrices.

A general theorem on factorization of matrices with polynomial entries is proven and it is used to reduce polynomial Darboux matrices to linear ones. Some new examples of linear Darboux matrices are discussed.

Leighton's graph covering theorem says that two finite graphs with a common cover have a common finite cover. We present a new proof of this using groupoids, and use this as a model to prove two generalisations of the theorem. The first…

Some identities of Chebyshev polynomials are deduced from Waring's formula on symmetric functions. In particular, these formulae generalize some recent results of Grabner and Prodinger.

\begin{abstract} We apply the theory of generalized Watson transforms developed in \cite{zheng00} to construct the complementary series of $GL(2,\R)$. \end{abstract}

We begin by explaining how arguments used by R. Wilson to give an elementary proof of the $\mathbb F_p$ case for the Ax-Katz Theorem can also be used to prove the following generalization of the Chevalley-Warning and Ax-Katz Theorems for…

In this paper we establish some subnormal embeddings of groups into groups with additional properties; in particular embeddings of countable groups into 2-generated groups with some extra properties. The results obtained are generalizations…