ぱらぱらめくる『Zeta Functions of Graphs』

Zeta Functions of Graphs: A Stroll through the Garden (Cambridge Studies in Advanced Mathematics)

Zeta Functions of Graphs: A Stroll through the Garden (Cambridge Studies in Advanced Mathematics)

  • 目次
    • Part I A quick look at various zeta functions
    • Part II Ihara zeta function and the graph theory prime number theorem
    • Part III Edge and path zeta functions
    • Part IV Finite unramified Galois coverings of connected graphs
    • Part V Last look at the garden
  • 細目次
    • Part I A quick look at various zeta functions
      • 1 Riemann zeta function and other zetas from number theory
      • 2 Ihara zeta function
      • 3 Selberg zeta function
      • 4 Ruelle zeta function
      • 5 Chaos
    • Part II Ihara zeta function and the graph theory prime number theorem
      • 6 Ihara zeta function of a weighted graph
      • 7 Regular graphs, location of poles of the Ihara zeta, functional equations
      • 8 Irregular graphs: what is the Riemann hypothesis?
      • 9 Discussion of regular Ramanujan graphs
      • 10 Graph theory prime number theorem
    • Part III Edge and path zeta functions
      • 11 Edge zeta functions
      • 12 Path zeta functions
    • Part IV Finite unramified Galois coverings of connected graphs
      • 13 Finite unramified coverings and Galois groups
      • 14 Fundamental theorem of Galois theory
      • 15 Behavior of primes in coverings
      • 16 Frobenius automorphisms
      • 17 How to construct intermediate coverings using the Frobenius automorphism
      • 18 Artin L-functions
      • 19 Drge Artin L-functions
      • 20 Path Artin L-functions
      • 21 Non-isomorphic regular graphs without loops or multiedges having the same Ihara zeta function
      • 22 Chebotarev density theorem
      • 23 Siegel poles
    • Part V Last look at the garden
      • 24 An application toerror-correcting codes
      • 25 Explicit formulas
      • 26 Again chaos
      • 27 Final research prblems