An unconditional GL large sieve

Large Sieve Inequalities for GL(n)-forms In the Conductor Aspect

Duke and Kowalski in [6] derive a large sieve inequality for automorphic forms on GL(n) via the Rankin-Selberg method. We give here a partial complement to this result: using some explicit geometry of fundamental regions, we prove a large sieve inequality yielding sharp results in a region distinct to that in [6]. As an application, we give a generalization to GL(n) of Duke’s multiplicity theor...

Bilinear Forms with Gl 3 Kloosterman Sums and the Spectral Large Sieve

We analyze certain bilinear forms involving GL3 Kloosterman sums. As an application, we obtain an improved estimate for the GL3 spectral large sieve inequality.

Large optical photon sieve.

A photon sieve with 10(7) holes has been constructed for operation at optical wavelengths. Details of the design, fabrication, and performance of this device are presented. The 1 m focal-length, 0.1 m diameter element is diffraction limited over a significant bandwidth and has a moderate field of view.

Notes on the large sieve

An Alternate Argument for the Arithmetic Large Sieve Inequality

the notation ∑[ and ∑∗ denoting, respectively, a sum over squarefree integers, and one over integers coprime with the (implicit) modulus, which is q here. By work of Montgomery-Vaughan and Selberg, it is known that one can take ∆ = Q − 1 +N (see, e.g., [IK, Th. 7.7]). There are a number of derivations of (1) from (2); for one of the earliest, see [M1, Ch. 3]. The most commonly used is probably ...