Related papers: A Lower Bound for the Large Sieve with Square Modu…
The purpose of this paper is twofold: 1) Applications of Gallagher's larger sieve modulo prime squares do not work. In some relevant cases we can transform the residue class information modulo $p^2$ to more suitable residue information…
In this very short note we prove a lower bound for the scalar curvature of certain steady gradient Ricci solitons.
We improve on the best available bounds for the square-free sieve and provide a general framework for its applicability. The failure of the local-to-global principle allows us to obtain results better than those reached by a classical…
We derive, for all prime moduli p except those in a very thin set, an upper bound for the least prime primitive root (mod p) of order of magnitude a constant power of log p. The improvement over previous results, where the upper bound was…
We give new, explicit and asymptotically sharp, lower bounds for dimensions of irreducible modular representations of finite symmetric groups.
In this paper we aim to generalize the results in Baier and Zhao and develop a general formula for large sieve with characters to powerful moduli that will be an improvement to the result of Zhao.
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…
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…
In this paper, we present an improvement of a large sieve type inequality in high dimensions and discuss its implications on a related problem.
We prove a sharp lower bound on the curvatures of non-flat ASD connections over the cylinder.
The goal of this paper is to improve existing bounds for Fourier coefficients of higher genus Siegel modular forms of small weight.
We introduce a variant of the large sieve and give an example of its use in a sieving problem. Take the interval [N] = {1,...,N} and, for each odd prime p <= N^{1/2}, remove or ``sieve out'' by all n whose reduction mod p lies in some…
We establish large sieve inequalities for power moduli in imaginary quadratic number fields, extending earlier work of Baier and Bansal for the Gaussian field.
We derive Moore-type upper bounds for regular simplicial complexes and present logarithmic lower bounds on their diameter based on minimum degree.
We show that the large sieve is optimal for almost all exponential sums, thus proving a conjecture by Erd\"os and Renyi.
We use the Burgess bound and Selberg sieve to obtain an upper bound on the second moment of sums over an interval $[u+1,u+h]$ of Legendre symbols modulo primes $p$ in a dyadic interval $[Q,2Q]$. The bound is nontrivial and gives a power…
We extend bounds on additive energies of modular square roots by Dunn, Kerr, Shparlinski, Shkredov and Zaharescu and apply these results to obtain bounds on certain bilinear exponential sums with modular square roots. From here, we make…
We study certain aspects of the Selberg sieve, in particular when sifting by rather thin sets of primes. We derive new results for the lower bound sieve suited especially for this setup and we apply them in particular to give a new…
We prove a result on lower bounds in large dimensions.
In this article, we establish a large sieve inequality for additive characters to moduli in the range of appropriate integer polynomials of degree two. As an application, we derive a weighted zero-density estimate for twists of…