Dynamical, Spectral, and Arithmetic Zeta Functions |  | Author: Michel L. Lapidus
Creator: Machiel Van Frankenhuysen
Publisher: American Mathematical Society
Category: Book
List Price: $51.00
Buy New: $35.44
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Sales Rank: 5071397
Media: Mass Market Paperback
Pages: 195
Number Of Items: 1
Shipping Weight (lbs): 0.8
Dimensions (in): 10.3 x 7.3 x 0.5
ISBN: 0821820796
Dewey Decimal Number: 515.56
EAN: 9780821820797
Publication Date: January 1, 2002
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Product Description
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.
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