Related papers: Multilinear Exponential Sums With A General Class …

In this paper we present a new family of identities for Euler sums and integrals of polylogarithms by using the methods of generating function and integral representations of series. Then we apply it to obtain the closed forms of all…

In this article, we consider the weighted partition function $p_f(n)$ given by the generating series $\sum_{n=1}^{\infty} p_f(n)z^n = \prod_{n\in\mathbb{N}^{*}}(1-z^n)^{-f(n)}$, where we restrict the class of weight functions to strongly…

We establish results with an arithmetic flavor that generalize the polynomial multidimensional Szemeredi theorem and related multiple recurrence and convergence results in ergodic theory. For instance, we show that in all these statements…

We bound the tensor ranks of elementary symmetric polynomials, and we give explicit decompositions into powers of linear forms. The bound is attained when the degree is odd.

In this article, we study the convergence behaviour of the classical generalized Max Product exponential sampling series in the weighted space of log-uniformly continuous and bounded functions. We derive basic convergence results for both…

We improve the known upper bound for short exponential sums and increase the range on which a sharp upper bound is known.

The aim of this paper is to generalize a main theorem concerning weighted mean summability to absolute matrix summability which plays a vital role in summability theory and applications to the other sciences by using quasi-$f$-power…

Generalized linear mixed models are powerful tools for analyzing clustered data, where the unknown parameters are classically (and most commonly) estimated by the maximum likelihood and restricted maximum likelihood procedures. However,…

Here we introduce a generalization of the exponential sampling series of optical physics and establish pointwise and uniform convergence theorem, also in a quantitative form. Moreover we compare the error of approximation for Mellin…

We establish upper and lower bounds with matching leading terms for tails of weighted sums of two-sided exponential random variables. This extends Janson's recent results for one-sided exponentials.

This is an expository survey on recent sum-product results in finite fields. We present a number of sum-product or "expander" results that say that if $|A| > p^{2/3}$ then some set determined by sums and product of elements of $A$ is nearly…

We use a generalization of Vinogradov's mean value theorem of S. Parsell, S. Prendiville and T. Wooley and ideas of W. Schmidt to give nontrivial bounds for the number of solutions to polynomial congruences, for arbitrary polynomials, when…

In this paper we introduce a new approach and obtain new results for the problem of studying polynomial images of affine subspaces of finite fields. We improve and generalise several previous known results, and also extend the range of such…

We prove an effective equidistribution result for a class of higher step nilflows, called filiform nilflows, and derive bounds on Weyl sums for higher degree polynomials with a power saving comparable to the best known, derived by J.…

We derive sharp Sobolev embeddings on a class of Sobolev spaces with potential weights without assuming any boundary conditions. Moreover, we consider the Adams-type inequalities for the borderline Sobolev embedding into the exponential…

We consider families of exponential sums indexed by a subgroup of invertible classes modulo some prime power $q$. For fixed $d$, we restrict to moduli $q$ so that there is a unique subgroup of invertible classes modulo $q$ of order $d$. We…

In this note we consider algebraic exponential sums over the values of homogeneous nonsingular polynomials $F(x_1, \cdots, x_n) \in \mathbb{Z}[x_1, \cdots, x_n]$ in the quotient ring $\mathbb{Z}/p^2\mathbb{Z}$. We provide an estimate of…

In this note, we presented a new decomposition of elements of finite fields of even order and illustrated that it is an effective tool in evaluation of some specific exponential sums over finite fields, the explicit value of some…

Let $q$ be a power of a prime and let $\mathbb{F}_q$ be the finite field consisting of $q$ elements. We establish new explicit estimates on Gauss sums of the form $S_n(a) = \sum_{x\in \mathbb{F}_q}\psi_a(x^n)$, where $\psi_a$ is a…

We examine exponential sums of the form $\sum_{n \le X} w(n) e^{2\pi i\alpha n^k}$, for $k=1,2$, where $\alpha$ satisfies a generalized Diophantine approximation and where $w$ are different arithmetic functions that might be multiplicative,…