Dynamical, spectral, and arithmetic zeta functions : AMS Special Session on Dynamical, Spectral, and Arithmetic Zeta Functions, January 15-16, 1999, San Antonio, Texas
著者
書誌事項
Dynamical, spectral, and arithmetic zeta functions : AMS Special Session on Dynamical, Spectral, and Arithmetic Zeta Functions, January 15-16, 1999, San Antonio, Texas
（Contemporary mathematics, v. 290）
American Mathematical Society, c2001
- タイトル別名
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Spectral and arithmetic zeta functions
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注記
Includes bibliographical references
内容説明・目次
内容説明
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 number-theoretic 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 number-theoretic 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 up-to-date research. It should be useful to both graduate students and confirmed researchers.
目次
Eigenfunctions of the transfer operators and the period functions for modular groups by C.-H. Chang and D. H. Mayer A note on dynamical trace formulas by C. Deninger and W. Singhof Small eigenvalues and Hausdorff dimension of sequences of hyperbolic three-manifolds by C. E. Fan and J. Jorgenson Dynamical zeta functions and asymptotic expansions in Nielsen theory by A. Fel'shtyn Computing the Riemann zeta function by numerical quadrature by W. F. Galway On Riemann's zeta function by S. Haran A prime orbit theorem for self-similar flows and Diophantine approximation by M. L. Lapidus and M. van Frankenhuysen The $10^{22}$-nd zero of the Riemann zeta function by A. M. Odlyzko Spectral theory, dynamics, and Selberg's zeta function for Kleinian groups by P. Perry On zeroes of automorphic $L$-functions by C. Soule Artin $L$-functions of graph coverings by H. M. Stark and A. A. Terras.
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