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 (which...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2011
|
| Series: | Cambridge studies in advanced mathematics
128 |
| Subjects: | |
| Online Access: | DE-12 DE-92 DE-355 Volltext |
| Summary: | 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. Created for beginning graduate students, the book will also appeal to researchers. Many well-chosen illustrations and exercises, both theoretical and computer-based, are included throughout |
| Physical Description: | 1 Online-Ressource (xii, 239 Seiten) |
| ISBN: | 9780511760426 |
| DOI: | 10.1017/CBO9780511760426 |
Staff View
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| indexdate | 2025-03-03T13:02:22Z |
| institution | BVB |
| isbn | 9780511760426 |
| language | English |
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| spelling | Terras, Audrey 1942- Verfasser (DE-588)115217320 aut Zeta functions of graphs a stroll through the garden Audrey Terras Cambridge Cambridge University Press 2011 1 Online-Ressource (xii, 239 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge studies in advanced mathematics 128 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. Created for beginning graduate students, the book will also appeal to researchers. Many well-chosen illustrations and exercises, both theoretical and computer-based, are included throughout Graph theory Functions, Zeta Zetafunktion (DE-588)4190764-4 gnd rswk-swf Zetafunktion (DE-588)4190764-4 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-11367-0 Cambridge studies in advanced mathematics 128 (DE-604)BV044781283 128 https://doi.org/10.1017/CBO9780511760426 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Terras, Audrey 1942- Zeta functions of graphs a stroll through the garden Cambridge studies in advanced mathematics Graph theory Functions, Zeta Zetafunktion (DE-588)4190764-4 gnd |
| subject_GND | (DE-588)4190764-4 |
| title | Zeta functions of graphs a stroll through the garden |
| title_auth | Zeta functions of graphs a stroll through the garden |
| title_exact_search | Zeta functions of graphs a stroll through the garden |
| title_full | Zeta functions of graphs a stroll through the garden Audrey Terras |
| title_fullStr | Zeta functions of graphs a stroll through the garden Audrey Terras |
| title_full_unstemmed | Zeta functions of graphs a stroll through the garden Audrey Terras |
| title_short | Zeta functions of graphs |
| title_sort | zeta functions of graphs a stroll through the garden |
| title_sub | a stroll through the garden |
| topic | Graph theory Functions, Zeta Zetafunktion (DE-588)4190764-4 gnd |
| topic_facet | Graph theory Functions, Zeta Zetafunktion |
| url | https://doi.org/10.1017/CBO9780511760426 |
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