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Zeta functions of graphs : a stroll through the garden /
"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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
2011.
|
| Colección: | Cambridge studies in advanced mathematics ;
128. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Terras, Audrey. | |
| 245 | 1 | 0 | |a Zeta functions of graphs : |b a stroll through the garden / |c Audrey Terras. |
| 260 | |a Cambridge ; |a New York : |b Cambridge University Press, |c 2011. | ||
| 300 | |a 1 online resource (xii, 239 pages) : |b illustrations (1 color) | ||
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| 490 | 1 | |a Cambridge studies in advanced mathematics ; |v 128 | |
| 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"-- |c Provided by publisher | ||
| 504 | |a Includes bibliographical references (pages 230-235) and index. | ||
| 505 | 0 | |a A quick look at various zeta functions. Riemann's zeta function and other zetas from number theory -- Ihara's zeta function -- Selberg's zeta function -- Ruelle's zeta function -- Chaos -- Ihara's zeta function and the graph theory prime number theorem. Ihara zeta function of a weighted graph -- Regular graphs, location of poles of zeta, functional equations -- Irregular graphs: what is the RH? -- Discussion of regular Ramanujan graphs -- The graph theory prime number theorem --Edge and path zeta functions. The edge zeta function -- Path zeta functions -- Finite unramified Galois coverings of connected graphs. Finite unramified coverings and Galois groups -- Fundamental theorem of Galois theory -- Behavior of primes in coverings -- Frobenius automorphisms -- How to construct intermediate coverings using the Frobenius automorphism -- Artin L-functions -- Edge Artin L-functions -- Path Artin L-functions -- Non-isomorphic regular graphs without loops or multiedges having the same Ihara zeta function -- The Chebotarev density theorem -- Siegel poles -- Last look at the garden. An application to error-correcting codes -- Explicit formulas -- Again chaos -- Final research problems. | |
| 588 | 0 | |a Print version record. | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Graph theory. | |
| 650 | 0 | |a Functions, Zeta. | |
| 650 | 6 | |a Fonctions zêta. | |
| 650 | 7 | |a MATHEMATICS |x Graphic Methods. |2 bisacsh | |
| 650 | 7 | |a Functions, Zeta |2 fast | |
| 650 | 7 | |a Graph theory |2 fast | |
| 650 | 7 | |a Graphentheorie |2 gnd | |
| 650 | 7 | |a Zetafunktion |2 gnd | |
| 776 | 0 | 8 | |i Print version: |a Terras, Audrey. |t Zeta functions of graphs. |d New York : Cambridge University Press, 2010 |z 9780521113670 |w (DLC) 2010024611 |w (OCoLC)639166318 |
| 830 | 0 | |a Cambridge studies in advanced mathematics ; |v 128. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=337707 |z Texto completo |
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