Zeta Functions of Graphs: A Stroll through the Garden

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