Related papers: The square sieve and the large sieve with square m…
We prove a lower bound for the large sieve with square moduli.
We establish a result on the large sieve with square moduli. These bounds impro ve recent results by S. Baier(math.NT/0512228) and L. Zhao(math.NT/0508125).
We prove an estimate for the large sieve with square moduli which improves a recent result of L. Zhao. Our method uses an idea of D. Wolke and some results from Fourier analysis.
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 revisit the large sieve for square moduli and obtain conditional improvements under hypotheses on higher additive energies of modular square roots.
We prove a lower and an upper bound for the large sieve with square moduli for function fields. These bounds correspond to bounds for the classical large sieve with square moduli established in arXiv:1812.05844 by Baier, Lynch and Zhao and…
We prove a large sieve inequality for square norm moduli in Z[i].
In this article, we obtain an explicit version of Heath-Brown's large sieve inequality for quadratic characters and discuss its applications to $L$-functions and quadratic fields.
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 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.
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…
In this paper, we develop a large sieve type inequality with quadratic amplitude. We use the double large sieve to establish non-trivial bounds.
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…
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 establish a large sieve inequality for power moduli in $\mathbb{Z}[i]$, extending earlier work by L. Zhao and the first-named author on the large sieve for power moduli for the classical case of moduli in $\mathbb{Z}$. Our method starts…
In this paper, we develop a large sieve type inequality with characters to square moduli. One expects that the result should be weaker than the classical inequality, but, conjecturally at least, not by much. The method is generalizable to…
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 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 generalise the square sieve developed by Heath-Brown to higher powers in order to improve on the error term for the problem of counting consecutive power-free numbers.