Related papers: Multiple Exponential and Character Sums with Monom…
This is an expository account of the proof of the theorem of Bourgain, Glibichuk and Konyagin which provides non-trivial bounds for exponential sums over very small multiplicative subgroups of prime finite fields.
We derive exponential bounds for tail of distribution for natural, i.e. under ordinary logarithm, normalized sums of arrays of random variables, not necessarily independent.
The extremal values of multivariate trigonometric polynomials are of interest in fields ranging from control theory to filter design, but finding the extremal values of such a polynomial is generally NP-Hard. In this paper, we develop…
In this paper, the formulas of some exponential sums over finite field, related to the Coulter's polynomial, are settled based on the Coulter's theorems on Weil sums, which may have potential application in the construction of linear codes…
This paper provides a technique for evaluating some nonlinear Gaussian sums in closed forms. The evaluation is obtained from the known values of simpler exponential sums.
For a prime number $p$ and integer $x$ with $\gcd(x,p)=1$ let $\overline{x}$ denote the multiplicative inverse of $x$ modulo $p.$ In the present paper we are interested in the problem of distribution modulo $p$ of the sequence $$…
The work of this paper is devoted to obtaining strong laws for intermediately trimmed sums of random variables with infinite means. Particularly, we provide conditions under which the intermediately trimmed sums of independent but not…
We combine a classical idea of Postnikov (1956) with the method of Korobov (1974) for estimating double Weyl sums, deriving new bounds on short character sums when the modulus $q$ has a small core $\prod_{p\mid q}p$. Using this estimate, we…
In this paper, we survey and refine several results -- some previously established in the literature -- that facilitate the construction of exponential bases on planar domains with explicit control over the associated frame bounds. We apply…
We consider binomial and inverse binomial sums at infinity and rewrite them in terms of a small set of constants, such as powers of $\pi$ or $\log(2)$. In order to perform these simplifications, we view the series as specializations of…
The problem of combining p-values is an old and fundamental one, and the classic assumption of independence is often violated or unverifiable in many applications. There are many well-known rules that can combine a set of arbitrarily…
In this article, we investigate conditional large values of quadratic Dirichlet character sums. We prove some Omega results of quadratic character sums under the assumption of the generalized Riemnn hypothesis, which are as sharp as…
We provide a unified, probabilistic approach using renewal theory to derive some novel limits of sums for the normalized binomial coefficients and for the normalized Eulerian numbers. We also investigate some corresponding results for their…
A survey paper on some recent results on additive problems with prime powers.
The expansion of bivariate polynomials is well-understood for sets with a linear-sized product set. In contrast, not much is known for sets with small sumset. In this work, we provide expansion bounds for polynomials of the form $f(x, y) =…
We study three classes of combinatorial sums involving central binomial coefficients and harmonic numbers, odd harmonic numbers, and even indexed harmonic numbers, respectively. In each case we use summation by parts to derive recursive…
We discuss various aspects of representation of a polynomial as a sum of monomials (for example, uniqueness of such representation and related estimations).
Studies of modular linear differential equations (MLDE) for the classification of rational CFT characters have been limited to the case where the coefficient functions (in monic form) have no poles, or poles at special points of moduli…
A polynomial is expansive if all of its roots lie outside the unit circle. We define some special determinants involving the coefficients of a real polynomial and formulate necessary and sufficient conditions for expansivity using these…
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.