@phdthesis{Srichan2015,
  author    = {Srichan, Teerapat},
  title     = {Discrete Moments of Zeta-Functions with respect to random and ergodic transformations},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-118395},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2015},
  abstract  = {In the thesis discrete moments of the Riemann zeta-function and allied Dirichlet series are studied. In the first part the asymptotic value-distribution of zeta-functions is studied where the samples are taken from a Cauchy random walk on a vertical line inside the critical strip. Building on techniques by Lifshits and Weber analogous results for the Hurwitz zeta-function are derived. Using Atkinson's dissection this is even generalized to Dirichlet L-functions associated with a primitive character. Both results indicate that the expectation value equals one which shows that the values of these zeta-function are small on average. The second part deals with the logarithmic derivative of the Riemann zeta-function on vertical lines and here the samples are with respect to an explicit ergodic transformation. Extending work of Steuding, discrete moments are evaluated and an equivalent formulation for the Riemann Hypothesis in terms of ergodic theory is obtained. In the third and last part of the thesis, the phenomenon of universality with respect to stochastic processes is studied. It is shown that certain random shifts of the zeta-function can approximate non-vanishing analytic target functions as good as we please. This result relies on Voronin's universality theorem.},
  subject      = {Riemannsche Zetafunktion},
  language  = {en}
}