A variant of the large sieve inequality with explicit constants

We give an effective version with explicit constants of the large sieve inequality for imaginary quadratic fields. Explicit results of this kind are useful for estimating the computational complexity of algorithms which generate elements, whose norm is a rational prime, in an arithmetic progression of the corresponding ring of integers.

The large sieve inequality with square moduli for quadratic extensions of function fields

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

Global decomposition of GL(3) Kloosterman sums and the spectral large sieve

We prove best-possible bounds for bilinear forms in Kloosterman sums for \operatorname{GL}(3) associated with the long Weyl element. As an application we derive a best-possible spectral large sieve inequality on \operatorname{GL}(3).

The large sieve with power moduli for ℤ[i]

We establish a large sieve inequality for power moduli in [Formula: see text], extending earlier work by Zhao and the first-named author on the large sieve for power moduli for the classical case of moduli in [Formula: see text]. Our method starts with a version of the large sieve for [Formula: see text]. We convert the resulting counting problem back into one for [Formula: see text] which we then attack using Weyl differencing and Poisson summation.