相关论文: Additive functions on shifted primes
Motivated by recent interests in predictive inference under distribution shift, we study the problem of approximating finite weighted exchangeable sequences by a mixture of finite sequences with independent terms. Various bounds are derived…
In this paper, we obtain uniform bounds for a number of expressions that involve derivatives and integrals of modified Bessel functions. These uniform bounds are motivated by the need to bound such expressions in the study of variance-gamma…
We estimate the concentration functions of $n$-fold convolutions of one-dimensional probability measures. The main result is a supplement to the results of G\"otze and Zaitsev (1998). We show that the estimation of concentration functions…
The aim of this work is to introduced the concept of the best one-sided approximation of unbounded functions in weighted space by using algebraic operators in terms the average modulus of smoothness. We also show an estimate of the degree…
The paper deals with studying a connection of the Littlewood--Offord problem with estimating the concentration functions of some symmetric infinitely divisible distributions.
We establish sharp upper bounds for shifted moments of quadratic Dirichlet $L$-function under the generalized Riemann hypothesis. Our result is then used to prove bounds for moments of quadratic Dirichlet character sums.
Estimates of some integrals related to variations of smooth functions are presented.
We consider the integration of two-dimensional, piecewise constant functions with respect to copulas. By drawing a connection to linear assignment problems, we can give optimal upper and lower bounds for such integrals and construct the…
We establish upper bounds for shifted moments of cubic and quartic Dirichlet $L$-functions under the generalized Riemann hypothesis. As an application, we prove bounds for moments of cubic and quartic Dirichlet character sums.
We reveal a relationship between the prime counting function and an operation performed on a unique subsequence of the primes.
We present some partial results regarding subadditivity of maximal shifts in finite graded free resolutions.
The purpose of the paper is to provide a characterization of the error of the best polynomial approximation of composite functions in weighted spaces. Such a characterization is essential for the convergence analysis of numerical methods…
Known Bernstein-type upper bounds on the tail probabilities for sums of independent zero-mean sub-exponential random variables are improved in several ways at once. The new upper bounds have a certain optimality property.
We prove a strong simultaneous Diophantine approximation theorem for values of additive and multiplicative functions provided that the functions have certain regularity on the primes.
Given a suitable arithmetic function h, we investigate the average order of h as it ranges over the values taken by an integral binary form F. A general upper bound is obtained for this quantity, in which the dependence upon the…
Some properties of integral averages of functions on intervals and their asymptotic behavior are investigated. The results are aimed at applications to entire and subharmonic functions.
We study concentration inequalities for structured weighted sums of random data, including (i) tensor inner products and (ii) sequential matrix sums. We are interested in tail bounds and concentration inequalities for those structured…
We first study subextensions of m-subharmonic functions in weighted energy classes with given boundary values. The results are used to approximate an m-subharmonic function in weighted energy classes with given boundary values by an…
We study sharpened forms of the concentration of measure phenomenon typically centered at stochastic expansions of order $d-1$ for any $d \in \mathbb{N}$. The bounds are based on $d$-th order derivatives or difference operators. In…
For 24 years, it has been an open problem to obtain improved bounds, for the maximal function over a sparse sequence of discrete spherical averages, going beyond the range for the full discrete spherical maximal function. I formulate a…