Related papers: A Tale of Three Coauthors
This is a survey of old and new problems and results in additive number theory.
We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. We use this bound to improve a series of previous results on various exponential sums and some arithmetic problems involving points on…
Certain new inequalities for the sums of factorials are presented.
We obtain upper bounds on the number of finite sets $\mathcal S$ of primes below a given bound for which various $2$ variable $\mathcal S$-unit equations have a solution.
We examine a family of three-dimensional exponential sums with monomials and provide estimates which are in some instances sharper than those stemming from approaches entailing the use of existing bounds pertaining to analogous sums.
We prove that the ratio of the Newman sum over numbers multiple of a fixed integer which is not multiple of 3 and the Newman sum over numbers multiple of a fixed integer divisible by 3 is o(1) when the upper limit of summing tends to…
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.
The aim of the present work is to show that recent results of the authors on the approximation of distributions of sums of independent summands by the infinitely divisible laws on convex polyhedra can be shown via an alternative class of…
We use an estimate of Aksoy Yazici, Murphy, Rudnev and Shkredov (2016) on the number of solutions of certain equations involving products and differences of sets in prime finite fields to give an explicit upper bound on trilinear…
We establish bounds of triple exponential sums with mixed exponential and linear function. The method we use is by Shparlinski together with a bound of additive energy from Roche-Newton, Rudnev and Shkredov.
We prove that Burgess's bound gives an estimate not just for a single character sum, but for a mean value of many such sums.
In this paper, we consider certain finite sums related to the "largest odd divisor", and we obtain, using simple ideas and recurrence relations, sharp upper and lower bounds for these sums.
Another approach to constructing an upper bound for the Riemann-Farey sum is described.
We give explicit bounds for the tail probabilities for sums of independent geometric or exponential variables, possibly with different parameters.
We estimate the lattice sums arising in the context of the integer point counting in polyhedra.
Finite trigonometric sums appear in various branches of Physics, Mathematics and their applications. For p; q to coprime positive integers and r we consider the finite trigonometric sums involving the product of three trigonometric…
We study bounds for correlation sums of automorphic coefficients on $\mathrm{GL}_{3,\mathbb{Q}}$ with trace functions of composite moduli. This is a sequel to our previous works with E. Kowalski and W. Sawin.
We obtain a new upper bound for binary sums with multiplicative characters over variables belong to some sets, having small additive doubling.
For W a finite Coxeter group, a formula is found for the size of W equivalence classes of subsets of a base. The proof is a case-by-case analysis using results and tables of Carter and Orlik/Solomon. As a corollary we obtain an alternating…
As far as algebraic properties are concerned, the usual addition on the class of ordinal numbers is not really well behaved; for example, it is not commutative, nor left cancellative etc. In a few cases, the natural Hessemberg sum is a…