Related papers: On the Thue-Vinogradov Lemma
We introduce a canonical isomorphism from the space of pure-type complex differential forms on a compact complex manifold to the one on its infinitesimal deformations. By use of this map, we generalize an extension formula in a recent work…
In this paper we use Euler-Seidel matrices method to find out some properties of exponential and geometric polynomials and numbers. Some known results are reproved and some new results are obtained.
We show how the Binomial Theorem can be used to continue the Riemann Zeta Function to the left hand half-plane. This method yields the explicit values of the function at non-positive integers in terms of the Bernoulli numbers.
We establish a Bombieri-Vinogradov theorem for sectors in real quadratic number fields.
We combine the Riemann-Hilbert approach with the techniques of Banach algebras to obtain an extension of Baxter's Theorem for polynomials orthogonal on the unit circle. This is accomplished by using the link between the negative Fourier…
We establish how the coefficients of a sparse polynomial system influence the sum (or the trace) of its zeros. As an application, we develop numerical tests for verifying whether a set of solutions to a sparse system is complete. These…
We study the explicit formula of Euler numbers and polynomials of higher order
We state and prove a generalization of the Poincar\'e-Hopf index theorem for manifolds with boundary. We then apply this result to non-vanishing complex vector fields.
For each graph, we construct a bigraded chain complex whose graded Euler characteristic is a version of the Tutte polynomial. This work is motivated by earlier work of Khovanov, Helme-Guizon and Rong, and others.
The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].
Three generalizations of the well-known Ceva's Theorem are given in this paper and some applications.
We prove a monodromy theorem for local vector fields belonging to a sheaf satisfying the unique continuation property. In particular, in the case of admissible regular sheaves of local fields defined on a simply connected manifold, we…
This note gives a new elementary proof of Poincar\'e-Miranda theorem based on Sard's theorem and the simple classification of one-dimensional manifolds.
In this note we extend the Gauss-Lucas theorem on the zeros of the derivative of a univariate polynomial to the case of sequences of univariate polynomials whose almost all zeros lie in a given convex bounded domain in C.
In this article, we continue our recent investigations on bilinear sums and additive energies with modular square roots. Here we improve our recent results for the case when the ranges of variables are large. We use these results to make…
An efficient evaluation method is described for polynomials in finite fields. Its complexity is shown to be lower than that of standard techniques when the degree of the polynomial is large enough. Applications to the syndrome computation…
In this article, we introduce combinatorial models for poly-Bernoulli polynomials and poly-Euler numbers of both kinds. As their applications, we provide combinatorial proofs of some identities involving poly-Bernoulli polynomials.
We prove stronger variants of a multiplier theorem of Kislyakov. The key ingredients are based on ideas of Kislaykov and the Kahane-Salem-Zygmund inequality. As a by-product we show various multiplier theorems for spaces of trigonometric…
We present an elementary method for proving enumeration formulas which are polynomials in certain parameters if others are fixed and factorize into distinct linear factors over Z. Roughly speaking the idea is to prove such formulas by…
In this paper, by the umbral calculus method, we give a remarkable congruence involving Appell polynomials. Some applications on derangement polynomials are also presented.