Contemporary Mathematics 2001; 195 pp; softcover Volume: 290 ISBN10: 0821820796 ISBN13: 9780821820797 List Price: US$57 Member Price: US$45.60 Order Code: CONM/290
 The original zeta function was studied by Riemann as part of his investigation of the distribution of prime numbers. Other sorts of zeta functions were defined for numbertheoretic purposes, such as the study of primes in arithmetic progressions. This led to the development of \(L\)functions, which now have several guises. It eventually became clear that the basic construction used for numbertheoretic zeta functions can also be used in other settings, such as dynamics, geometry, and spectral theory, with remarkable results. This volume grew out of the special session on dynamical, spectral, and arithmetic zeta functions held at the annual meeting of the American Mathematical Society in San Antonio, but also includes four articles that were invited to be part of the collection. The purpose of the meeting was to bring together leading researchers, to find links and analogies between their fields, and to explore new methods. The papers discuss dynamical systems, spectral geometry on hyperbolic manifolds, trace formulas in geometry and in arithmetic, as well as computational work on the Riemann zeta function. Each article employs techniques of zeta functions. The book unifies the application of these techniques in spectral geometry, fractal geometry, and number theory. It is a comprehensive volume, offering uptodate research. It should be useful to both graduate students and confirmed researchers. Readership Graduate students and research mathematicians interested in number theory. Table of Contents  C.H. Chang and D. H. Mayer  Eigenfunctions of the transfer operators and the period functions for modular groups
 C. Deninger and W. Singhof  A note on dynamical trace formulas
 C. E. Fan and J. Jorgenson  Small eigenvalues and Hausdorff dimension of sequences of hyperbolic threemanifolds
 A. Fel'shtyn  Dynamical zeta functions and asymptotic expansions in Nielsen theory
 W. F. Galway  Computing the Riemann zeta function by numerical quadrature
 S. Haran  On Riemann's zeta function
 M. L. Lapidus and M. van Frankenhuysen  A prime orbit theorem for selfsimilar flows and Diophantine approximation
 A. M. Odlyzko  The \(10^{22}\)nd zero of the Riemann zeta function
 P. Perry  Spectral theory, dymamics, and Selberg's zeta function for Kleinian groups
 C. Soulé  On zeroes of automorphic \(L\)functions
 H. M. Stark and A. A. Terras  Artin \(L\)functions of graph coverings
