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)
- 作者: Audrey Terras
- 出版社/メーカー: Cambridge University Press
- 発売日: 2010/11/18
- メディア: ハードカバー
- クリック: 1回
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- 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
- Part I A quick look at various zeta functions