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...
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| Autor Principal: | |
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| Formato: | Libro |
| Idioma: | English |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
2011.
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| Series: | Cambridge studies in advanced mathematics ;
128 |
| Materias: | |
| Acceso en línea: | Publisher description Table of contents |
| Etiquetas: |
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| Sumario: | "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, are included throughout."-- |
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| Descripción Física: | xii, 239 p. : il. ; 24 cm. |
| Bibliografía: | Incluye referencias bibliográficas (p. 230-235) e índice. |
| ISBN: | 9780521113670 |