Related papers: A Variational Barban-Davenport-Halberstam Theorem

We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular we consider conservative nonlinear oscillators and a bifurcation problem. In the former case we obtain the same main result…

We prove new large sieve inequalities for the Fourier coefficients $\rho_{j\mathfrak{a}}(n)$ of exceptional Maass forms of a given level, weighted by sequences $(a_n)$ with sparse Fourier transforms - including two key types of sequences…

Inference is the task of drawing conclusions about unobserved variables given observations of related variables. Applications range from identifying diseases from symptoms to classifying economic regimes from price movements. Unfortunately,…

In this paper, we investigate the large deviations of sums of weighted random variables that are approximately independent, generalizing and improving some of the results of Montgomery and Odlyzko. We are motivated by examples arising from…

We provide a Lyapunov type bound in the multivariate central limit theorem for sums of independent, but not necessarily identically distributed random vectors. The error in the normal approximation is estimated for certain classes of sets,…

We provide variants and improvements of the Brascamp-Lieb variance inequality which take into account the invariance properties of the underlying measure. This is applied to spectral gap estimates for log-concave measures with many…

In this short note we establish new refinements of multidimensional Szemeredi and polynomial van der Waerden theorems along the shifted primes.

We establish the first mathematically rigorous link between Bayesian, variational Bayesian, and ensemble methods. A key step towards this it to reformulate the non-convex optimisation problem typically encountered in deep learning as a…

We give a simple inequality for the sum of independent bounded random variables. This inequality improves on the celebrated result of Hoeffding in a special case. It is optimal in the limit where the sum tends to a Poisson random variable.

We establish a general large sieve inequality with sparse sets $\mathcal{S}$ of moduli in the Gaussian integers which are in a sense well-distributed in arithmetic progressions. This extends earlier work of S. Baier on the large sieve with…

Motivated by applications to the study of L-functions, we develop an asymptotic version of the large sieve inequality for linear forms in primitive Dirichlet characters.

Using sieves and elementary manipulations, we show that the signs of partial sums of the Liouville function over divisors are in a strong sense equally distributed.

In this paper, we establish some theorems on the distribution of primes in higher-order progressions on average.

We represent in this preprint the exact estimate for covariation berween two random variables (r.v.), which are measurable relative the corresponding sigma-algebras through anyhow mixing coefficients. We associate a solution of this problem…

A Bernstein-von Mises theorem is derived for general semiparametric functionals. The result is applied to a variety of semiparametric problems in i.i.d. and non-i.i.d. situations. In particular, new tools are developed to handle…

We report the results of our empirical investigations on the Bateman-Horn conjecture. This conjecture, in its commonly known form, produces rather large deviations when the polynomials involved are not monic. We propose a modified version…

We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include a partitioning theorem, estimates on polynomials vanishing on fixed sets and bounds for the number of connected components of real algebraic…

We improve on the spectral large sieve inequality for symmetric-squares. We also prove a lower bound showing that the most optimistic upper bound is not true for this family.

We consider series of the form $\sum a_n \{n\cdot x\}$, where $n\in\Z^{d}$ and $\{x\}$ is the sawtooth function. They are the natural multivariate extension of Davenport series. Their global (Sobolev) and pointwise regularity are studied…

This paper investigates equivalence of square multivariate polynomial matrices with the determinant being some power of a univariate irreducible polynomial. We first generalized a global-local theorem of Vaserstein. Then we proved these…