Zeta functions of graphs : a stroll through the garden / Audrey Terras.
"Graph theory meets number theory in this stimulating book. Ihara zeta functions of finite graphs are reciprocals of polynomials, sometimes in several variables. Analogies abound with number-theoretic functions such as Riemann/Dedekind zeta functions. For example, there is a Riemann hypothesis (whic...
Saved in:
| Main Author: | |
|---|---|
| Language: | English |
| Published: |
Cambridge, UK ; New York :
Cambridge University Press,
2011.
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| Series: | Cambridge studies in advanced mathematics ;
128. |
| Subjects: | |
| Local Note: |
This resource was acquired with funds from Office of the Provost, Michigan State University, in honor of Professor Edgar M. Palmer, who retired from the Department of Mathematics in 2011. |
| Physical Description: | xii, 239 pages : illustrations (some color) ; 24 cm. |
| Format: | Book |
MARC
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| 020 | |a 0521113679 (hardback) | ||
| 035 | |a (CaEvSKY)sky235086967 | ||
| 035 | |a (OCoLC)639166318 | ||
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| 100 | 1 | |a Terras, Audrey. |0 http://id.loc.gov/authorities/names/n84172127 | |
| 245 | 1 | 0 | |a Zeta functions of graphs : |b a stroll through the garden / |c Audrey Terras. |
| 260 | |a Cambridge, UK ; |a New York : |b Cambridge University Press, |c 2011. | ||
| 300 | |a xii, 239 pages : |b illustrations (some color) ; |c 24 cm. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a unmediated |b n |2 rdamedia | ||
| 338 | |a volume |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge studies in advanced mathematics ; |v 128 | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 8 | |a Machine generated contents note: 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 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. | |
| 520 | |a "Graph theory meets number theory in this stimulating book. Ihara zeta functions of finite graphs are reciprocals of polynomials, sometimes in several variables. Analogies abound with number-theoretic functions such as Riemann/Dedekind zeta functions. For example, there is a Riemann hypothesis (which may be false) and prime number theorem for graphs. Explicit constructions of graph coverings use Galois theory to generalize Cayley and Schreier graphs. Then non-isomorphic simple graphs with the same zeta are produced, showing you cannot hear the shape of a graph. The spectra of matrices such as the adjacency and edge adjacency matrices of a graph are essential to the plot of this book, which makes connections with quantum chaos and random matrix theory, plus expander/Ramanujan graphs of interest in computer science. Pitched at beginning graduate students, the book will also appeal to researchers. Many well-chosen illustrations and diagrams, and exercises throughout, theoretical and computer-based"--Provided by publisher. | ||
| 590 | |a This resource was acquired with funds from Office of the Provost, Michigan State University, in honor of Professor Edgar M. Palmer, who retired from the Department of Mathematics in 2011. | ||
| 650 | 0 | |a Graph theory. |0 http://id.loc.gov/authorities/subjects/sh85056471 | |
| 650 | 0 | |a Functions, Zeta. |0 http://id.loc.gov/authorities/subjects/sh85052354 | |
| 830 | 0 | |a Cambridge studies in advanced mathematics ; |v 128. |0 http://id.loc.gov/authorities/names/n84708314 | |
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| 952 | f | f | |p Can Circulate |a Michigan State University-Library of Michigan |b Michigan State University |c MSU Main Library |d MSU Main Library |t 0 |e QA166 .T47 2011 |h Library of Congress classification |i Printed Material |m 31293007145448 |n 1 |