Dynamical zeta functions are associated to dynamical systems with a
countable set of periodic orbits. The dynamical zeta functions of
the geodesic flow of lo cally symmetric spaces of rank one are
known also as the generalized Selberg zeta functions. The present
book is concerned with these zeta functions from a cohomological
point of view. Originally, the Selberg zeta function appeared in
the spectral theory of automorphic forms and were suggested by an
analogy between Weil's explicit formula for the Riemann zeta
function and Selberg's trace formula ( 261]). The purpose of the
cohomological theory is to understand the analytical properties of
the zeta functions on the basis of suitable analogs of the
Lefschetz fixed point formula in which periodic orbits of the
geodesic flow take the place of fixed points. This approach is
parallel to Weil's idea to analyze the zeta functions of pro
jective algebraic varieties over finite fields on the basis of
suitable versions of the Lefschetz fixed point formula. The
Lefschetz formula formalism shows that the divisors of the rational
Hassc-Wcil zeta functions are determined by the spectra of
Frobenius operators on l-adic cohomology."
General
| Imprint: |
Springer Basel
|
| Country of origin: |
Switzerland |
| Series: |
Progress in Mathematics, 194 |
| Release date: |
October 2012 |
| First published: |
2001 |
| Authors: |
Andreas Juhl
|
| Dimensions: |
235 x 155 x 36mm (L x W x T) |
| Format: |
Paperback
|
| Pages: |
709 |
| Edition: |
Softcover reprint of the original 1st ed. 2001 |
| ISBN-13: |
978-3-03-489524-8 |
| Categories: |
Books >
Science & Mathematics >
Mathematics >
Calculus & mathematical analysis >
General
|
| LSN: |
3-03-489524-0 |
| Barcode: |
9783034895248 |
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