Treffer: THE PRIME GEODESIC THEOREM AND QUANTUM MECHANICS ON FINITE VOLUME GRAPHS: A REVIEW: The prime geodesic theorem and quantum mechanics on finite volume graphs: a review
Title:
THE PRIME GEODESIC THEOREM AND QUANTUM MECHANICS ON FINITE VOLUME GRAPHS: A REVIEW: The prime geodesic theorem and quantum mechanics on finite volume graphs: a review
Authors:
Source:
Reviews in Mathematical Physics. 13:1459-1503
Publisher Information:
World Scientific Pub Co Pte Lt, 2001.
Publication Year:
2001
Subject Terms:
Selberg-Ihara zeta function, Selberg zeta functions and regularized determinants, applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas), Selberg trace formula for finite graphs, Hecke operators, quantum mechanics on finite graphs, Spectral theory, trace formulas (e.g., that of Selberg), General mathematical topics and methods in quantum theory, Axiom A flows, 0101 mathematics, 01 natural sciences, Selberg eigenvalue conjecture
Document Type:
Fachzeitschrift
Article
File Description:
application/xml
Language:
English
ISSN:
1793-6659
0129-055X
0129-055X
DOI:
10.1142/s0129055x01001009
Access URL:
Accession Number:
edsair.doi.dedup.....5581e9c4b79e3919e882c2df83cfef3f
Database:
OpenAIRE
Weitere Informationen
The prime geodesic theorem is reviewed for compact and finite volume Riemann surfaces and for finite and finite volume graphs. The methodology of how these results follow from the theory of the Selberg zeta function and the Selberg trace formula is outlined. Relationships to work on quantum graphs are surveyed. Extensions to compact Riemannian manifolds, in particular to three-dimensional hyperbolic spaces, are noted. Interconnections to the Selberg eigenvalue conjecture, the Ramanujan conjecture and Ramanujan graphs are developed.