Seminar Details

This talk is based on a published paper of the same title that can be found here, The paper considers, both analytically and numerically, an integral Z(\sigma,r) related to the mean value of a generalized moment of Riemann's Zeta function. Analytically, we predict finite, but discontinuous values and verify the prediction numerically, employing a modified form of Cesà ro summation. Further, it is proven by analytic continuation and verified numerically that the derivative function equates to one generalized tine of the Dirac comb function. A surprising outcome of the numerical study arises from the observation that the proper integral form of the derivative function is quasi-periodic, which in turn suggests a periodicity of the integrand. This possibility is explored and it is found experimentally that Zeta function values offset (shifted) over certain segments of the imaginary complex number line are moderately auto-correlated.