Related papers: On the spectral large sieve inequality for symmetr…
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…
We prove a lower bound for the large sieve with square moduli.
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 formulate and prove a large sieve inequality for quadratic characters over a number field. To do this, we introduce the notion of an n-th order Hecke family. We develop the basic theory of these Hecke families, including versions of the…
In this paper, we introduce concise expressions for the complex Bessel integral that enables us to improve the spectral large sieve inequality of Watt for $\mathrm{PGL}_2 (\mathbb{Z}[i]) \backslash \mathrm{PGL}_2 (\mathbb{C})$. Our result…
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…
In this paper, we improve the error term in the prime geodesic theorem for the Picard manifold $ \mathrm{PSL}_2 (\mathbb{Z} {[i]}) \backslash \mathbb{H}^3 $. Instead of $ \mathrm{PSL}_2 (\mathbb{Z} {[i]}) \backslash \mathbb{H}^3 $, we…
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.
In this paper, we develop a large sieve type inequality for some special characters whose moduli are squares of primes. Our result gives non-trivial estimate in certain ranges.
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.
We provide here a modest improvement upon a large sieve inequality for quadratic polynomial amplitudes orginally due to Liangyi Zhao.
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 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).
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.
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 establish a version of the large sieve with square moduli for imaginary quadratic extensions of rational function fields of odd characteristics.
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…
We prove a large sieve inequality for square norm moduli in Z[i].
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…