25,980 research outputs found
On the Hecke Eigenvalues of Maass Forms
Let denote a primitive Hecke-Maass cusp form for with
the Laplacian eigenvalue . In this work we show
that there exists a prime such that , , and , where are the
Satake parameters of at , and is an absolute constant with
. In fact, can be taken as . In addition, we prove that the
natural density of such primes ( and ) is at least .Comment: Version 2: typos corrected and a new section on natural density adde
Spectral characterization of a specific class of trees
In this paper, it is shown that the graph is determined by its
Laplacian spectrum and there are no two non-isomorphic such graphs which are
cospectral with respect to adjacency spectrum.Comment: 11 pages, 4 figure
Superlensing properties of one-dimensional dielectric photonic crystals
We present the experimental observation of the superlensing effect in a slab
of a one-dimensional photonic crystal made of tilted dielectric elements. We
show that this flat lens can achieve subwavelength resolution in different
frequency bands. We also demonstrate that the introduction of a proper
corrugation on the lens surface can dramatically improve both the transmission
and the resolution of the imaged signal.Comment: 9 pages, 9 figure
- …