For 0 < a ? 1 / 2 , we define the quadrilateral zeta function Q ( s ) using Hurwitz and periodic functions show that satisfies Riemann's functional equation studied by Hamburger, Heck Knopp. Moreover, prove for any there exist positive constants A T such number of zeros on line segment from 1/2 to + i is greater than whenever ? .

Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, Research Campus Golm, D-14424 Potsdam, Germany, Stranski Laboratory of Physical and Theoretical Chemistry, Technical University Berlin, Straße des 17. Juni 135, D-10623 Berlin, Germany, and Hamburger Synchrotronstrahlungslabor (HASYLAB), Deutsches Elektronen-Synchrotron (DESY), Notkestraße 85, D-22603 Hamburg, Germany....

A calculation formula is established for the codimension of the polynomial subspace in L2(R, dμ) with discrete indeterminate measure μ. We clarify how much the masspoint of the n-canonical solution of an indeterminate Hamburger moment problem differs from the masspoint of the corresponding N-extremal solution at a given point of the real axis.