内容

目次

List of illustrations; Preface; Part I. A Quick Look at Various ZetaFunctions: 1. Riemann's zeta function and other zetas from number theory; 2.Ihara's zeta function; 3. Selberg's zeta function; 4. Ruelle's zeta function;5. Chaos; Part II. Ihara's Zeta Function and the Graph Theory Prime NumberTheorem: 6. Ihara zeta function of a weighted graph; 7. Regular graphs,location of poles of zeta, functional equations; 8. Irregular graphs: what isthe RH?; 9. Discussion of regular Ramanujan graphs; 10. The graph theoryprime number theorem; Part III. Edge and Path Zeta Functions: 11. The edgezeta function; 12. Path zeta functions; Part IV. Finite Unramified GaloisCoverings of Connected Graphs: 13. Finite unramified coverings and Galoisgroups; 14. Fundamental theorem of Galois theory; 15. Behavior of primes incoverings; 16. Frobenius automorphisms; 17. How to construct intermediatecoverings using the Frobenius automorphism; 18. Artin L-functions; 19. EdgeArtin L-functions; 20. Path Artin L-functions; 21. Non-isomorphic regulargraphs without loops or multiedges having the same Ihara zeta function; 22.The Chebotarev Density Theorem; 23. Siegel poles; Part V. Last Look at theGarden: 24. An application to error-correcting codes; 25. Explicit formulas;26. Again chaos; 27. Final research problems; References; Index.