Related papers: The Large Sieve Inequality for Integer Polynomial …

In this article, we give an account of some recent irreducibility testing criteria for polynomials having integer coefficients over the field of rational numbers.

We derive a large deviation principle for the empirical measure of zeros of random polynomials with i.i.d. exponential coefficients.

We establish an explicit inequality for the number of divisors of an integer $n$. It uses the size of $n$ and its number of distinct prime divisors.

We study several related problems on polynomials with integer coefficients. This includes the integer Chebyshev problem, and the Schur problems on means of algebraic numbers. We also discuss interesting applications to approximation by…

We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an…

Let $f$ be a polynomial of degree $d>6$, with integer coefficients. Then the paucity of non-trivial positive integer solutions to the equation $f(a)+f(b)=f(c)+f(d)$ is established. The corresponding situation for equal sums of three like…

We complement the argument of M. Z. Garaev (2009) with several other ideas to obtain a stronger version of the large sieve inequality with sparse exponential sequences of the form $\lambda^{s_n}$. In particular, we obtain a result which is…

We improve the large sieve inequality with $k$th-power moduli, for all $k\ge 4$. Our method relates these inequalities to a restricted variant of Waring's problem. Firstly, we input a classical divisor bound on the number of representations…

In this paper we prove several inequalities for binomial coefficients. For instance, if $ k$ and $n$ are positive integers such that $n\ge 400$ and $[\frac n5]\le k\le [\frac n2]$, where $[x]$ is the greatest integer not exceeding $x$, then…

We prove an essentially optimal large sieve inequality for self-dual Eisenstein series of varying levels. This bound can alternatively be interpreted as a large sieve inequality for rationals ordered by height. The method of proof is…

We give a new bound for the large sieve inequality with power moduli q^k that is uniform in k. The proof uses a new theorem due to T. Wooley from his work on efficient congruencing.

In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.

Suppose that an infinite set $A$ occupies at most $\frac{1}{2}(p+1)$ residue classes modulo $p$, for every sufficiently large prime $p$. The squares, or more generally the integer values of any quadratic, are an example of such a set. By…

In this paper, we establish a version of the large sieve with square moduli for imaginary quadratic extensions of rational function fields of odd characteristics.

We solve a Lehmer-type question about the Mahler measure of integer-valued polynomials.

In this note we give a new bound for large sieve with characters to power moduli which improves in some range of the parameters the previous bounds of Baier/Zhao and Halupczok.

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.

In this work a local inequality is provided which bounds the distance of an integral varifold from a multivalued plane (height) by its tilt and mean curvature. The bounds obtained for the exponents of the Lebesgue spaces involved are shown…

We describe a very general abstract form of sieve based on a large sieve inequality which generalizes both the classical sieve inequality of Montgomery (and its higher-dimensional variants), and our recent sieve for Frobenius over function…

Let $\lambda$ be a fixed integer, $\lambda\ge 2.$ Let $s_n$ be any strictly increasing sequence of positive integers satisfying $s_n\le n^{15/14+o(1)}.$ In this paper we give a version of the large sieve inequality for the sequence…