Riemann's Hypothesis

Riemann’s memoir is devoted to the function π(x) defined as the number of prime numbers less or equal to the real and positive number x. This is really the fact, but the “main role” in it is played by the already mentioned zeta-function

Complete Systems of Hermite Associated Functions

It is proved that if the increasing sequence {kn} n=0..∞ n=0 of nonnegative integers has density greater than 1/2 and D is an arbitrary simply connected subregion of C\R then the system of Hermite associated functions Gkn(z) n=0..∞ is complete in the space H(D) of complex functions holomorphic in D

A Note on a Classical Generating Function for the Jacobi Polynomials

Mathematics Subject Classification: 33C45.A more general form for a classical generating function for the Jacobi polynomials is given.* Partially supported by Project MM 1305 - National Science Fund, Bulgarian Ministry of Educ. Sci

Pygmy dipole strength close to particle-separation energies - the case of the Mo isotopes

The distribution of electromagnetic dipole strength in 92, 98, 100 Mo has been investigated by photon scattering using bremsstrahlung from the new ELBE facility. The experimental data for well separated nuclear resonances indicate a transition from a regular to a chaotic behaviour above 4 MeV of excitation energy. As the strength distributions follow a Porter-Thomas distribution much of the dipole strength is found in weak and in unresolved resonances appearing as fluctuating cross section. An analysis of this quasi-continuum - here applied to nuclear resonance fluorescence in a novel way - delivers dipole strength functions, which are combining smoothly to those obtained from (g,n)-data. Enhancements at 6.5 MeV and at ~9 MeV are linked to the pygmy dipole resonances postulated to occur in heavy nuclei.Comment: 6 pages, 5 figures, proceedings Nuclear Physics in Astrophysics II, May 16-20, Debrecen, Hungary. The original publication is available at www.eurphysj.or

Photon data shed new light upon the GDR spreading width in heavy nuclei

A global study of the electric dipole strength in and below the isovector giant dipole resonance (GDR) is presented for mass numbers A>80. It relies on the recently established remarkably good match between data for the nuclear photo effect to novel photon scattering data covering the region below the neutron emission threshold as well as by average resonance neutron capture (ARC). From the wide energy coverage of these data the correlation of the GDR spreading width with energy can be studied with remarkable accuracy. A clear sensitivity to details of the nuclear shape, i.e. the beta- and gamma-deformations, is demonstrated. Based hereon a new parameterization of the energy dependence of the nuclear electric-dipole strength is proposed which - with only two new parameters - allows to describe the dipole strength in all heavy nuclei with A>80. Although it differs significantly from previous parameterizations it holds for spherical, transitional, triaxial and well deformed nuclei. The GDR spreading width depends in a regular way on the respective resonance energy, but it is independent of the photon energy.Comment: accepted by Phys. Lett. B after minor modification