Related papers: Large sieve inequality for power moduli

We give a short alternative proof using Heath-Brown's square sieve of a bound of the author for the large sieve with square moduli.

In this paper, we prove a large sieve inequality for quartic Dirichlet characters. The result is analogous to large sieve inequalities for the quadratic and cubic Dirichlet characters.

In this paper, we present an improvement of a large sieve type inequality in high dimensions and discuss its implications on a related problem.

Extending a method of D. Wolke, we establish a general result on the large sieve with sparse sets S of moduli which are in a sense well-distributed in arithmetic progressions. We then use this result together with Fourier techniques to…

We present a new proof of the "arithmetic" large sieve inequality, starting from the corresponding "harmonic" inequality, which is based on an amplification idea. We show that this also adapts to give some new sieve inequality for modular…

In this paper we obtain a sharp upper bound for the number of solutions to a certain diophantine inequality involving fractions with power denominator. This problem is motivated by a conjecture of Zhao concerning the spacing of such…

We obtain a small improvement of Gallagher's larger sieve and we extend it to higher dimensions. We also obtain two interesting upper bounds for the number of solutions to polynomial congruences.

We prove large sieve inequalities with multivariate polynomial moduli and deduce a general Bombieri--Vinogradov type theorem for a class of polynomial moduli having a sufficient number of variables compared to its degree. This sharpens…

We provide here a modest improvement upon a large sieve inequality for quadratic polynomial amplitudes orginally due to Liangyi Zhao.

The goal of this paper is to improve existing bounds for Fourier coefficients of higher genus Siegel modular forms of small weight.

We prove an improved spectral large sieve inequality for the family of $SL_3(\mathbb{Z})$ Hecke-Maass cusp forms. The method of proof uses duality and its structure reveals unexpected connections to Heath-Brown's large sieve for cubic…

We combine Hooley neutralisers and the large sieve for quadratic characters. We give applications to character sums with a hyperbolic height condition.

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…

We obtain a close to the best possible version of the large sieve inequality with amplitudes given by the values of a polynomial with integer coefficients of degree $\geq 2$.

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 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…

Extending a method of D. Wolke, we establish a general result on the large sieve with sparse sets S of moduli which are in a sense well-distributed in arithmetic progressions. We then apply our result to the case when S consists of sqares.…

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 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 propose upper bounds for the number of modular constituents of the restriction modulo $p$ of a complex irreducible character of a finite group, and for its decomposition numbers, in certain cases.