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1 |
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|a Terras, Audrey.
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| 245 |
1 |
0 |
|a Zeta functions of graphs :
|b a stroll through the garden /
|c Audrey Terras.
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| 260 |
|
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|a Cambridge ;
|a New York :
|b Cambridge University Press,
|c 2011.
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| 300 |
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|a xii, 239 p. :
|b ill. (some col.) ;
|c 24 cm.
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| 490 |
1 |
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|a Cambridge studies in advanced mathematics ;
|v 128
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| 504 |
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|a Includes bibliographical references (p. 230-235) and index.
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| 505 |
0 |
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|a Part I. A Quick Look at Various Zeta Functions: 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 Number Theorem: 6. Ihara zeta function of a weighted graph; 7. Regular graphs, location of poles of zeta, functional equations; 8. Irregular graphs: what is the RH?; 9. Discussion of regular Ramanujan graphs; 10. The graph theory prime number theorem; Part III. Edge and Path Zeta Functions: 11. The edge zeta function; 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. Edge Artin L-functions; 20. Path Artin L-functions; 21. Non-isomorphic regular graphs without loops or multiedges having the same Ihara zeta function; 22. The Chebotarev Density Theorem; 23. Siegel poles; Part V. Last Look at the Garden: 24. An application to error-correcting codes; 25. Explicit formulas; 26. Again chaos; 27. Final research problems; References; Index.
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| 650 |
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|a Graph theory.
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| 650 |
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|a Functions, Zeta.
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| 830 |
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|a Cambridge studies in advanced mathematics ;
|v 128.
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| 856 |
4 |
2 |
|3 Contributor biographical information
|u http://catdir.loc.gov/catdir/enhancements/fy1108/2010024611-b.html
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