Zeta-Funktionen in der Physik - eine Einführung

"Zetafunctions in Physics - an Introduction" is an introductory monograph about Riemann-Zetafunction, Spectral Zetafunctions and Dynamical Zetafunctions in Physics on an advanced undergraduate level. Topics are: harmonic oszillator (not much surprising), phase operators and coherent states, pathintegrals of single- and many-particle systems, regularization with Spectral Zetafunction and Casimir-effect, heat-kernel-expansion and regularization and renormalization of the Phi(4,4)-theory in 1-loop approximation, Dynamical or Ruelle Zetafunctions in dynamical systems and Gutzwillers traceformula. Mathematical appendices deal with: Gammafunction, Riemann-Zetafunction, Mellin-transformation, asymptotic expansions, heat-kernel-expansion and (analytic) index-theorem for elliptic differential operators, Fredholm-theory of elliptic pseudo-differential operators. Due to the didactic intention of this introduction all proofs are worked out in details. So, enjoy yourself