Upper bounds of some special zeros for the Rankin-Selberg L-function

In this paper, we prove some conditional results about the order of zero at central point s = 1/2 of the Rankin-Selberg L-function L(s, πf × π͠′f). Then, we give an upper bound for the height of the first zero with positive imaginary part of L(s, πf × π͠′f). We apply our results to automorphic L-functions.

Description of the structure of singular spectrum for Friedrichs model operator near singular point

The study of the point spectrum and the singular continuous one is reduced to investigating the structure of the real roots set of an analytic function with positive imaginary partM(λ). We prove a uniqueness theorem for such a class of analytic functions. Combining this theorem with a lemma on smoothness ofM(λ)near its real roots permits us to describe the density of the singular spectrum.

HÖLDER ESTIMATES FOR THE ELASTIC FAR-FIELD PATTERN WITH RESPECT TO THE BOUNDARY

We prove that under a small perturbation (in the Euclidean metric) of the boundary of a Lipschitz domain there corresponds a small variation (in the uniform norm) of the elastic far-field pattern. The corresponding estimate is of Hölder type. This is done under the assumptions that the Lipschitz character of the perturbation is bounded and that the frequency of the elastic waves is either sufficiently small or has a strictly positive imaginary part.