Screen LibraryZeta functions of graphs：a stroll through the garden
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| Main Authors: | |
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| Published: |
Cambridge University Press,
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| Publisher Address: | Cambridge New York |
| Publication Dates: | 2011. |
| Literature type: | Book |
| Language: | English |
| Series: |
Cambridge studies in advanced mathematics ; 128 |
| Subjects: | |
| Carrier Form: | xii, 239 p.: ill. ; 24 cm. |
| ISBN: |
9780521113670 (hc.) 0521113679 |
| Index Number: | O157 |
| CLC: | O157.5 |
| Call Number: | O157.5/T324 |
| Contents: |
Includes bibliographical references (p. 230-235) and index. Riemann zeta function and other zetas from number theory -- Ihara zeta function -- Selberg zeta function -- Ruelle zeta function -- Chaos -- Ihara zeta function of a weighted graph -- Regular graphs, location of poles of the Ihara zeta, functional equations -- Irregular graphs: what is the Riemann hypothesis? -- Discussion of regular Ramanujan graphs -- Graph theory prime number theorem -- Edge zeta functions -- Path zeta functions -- Finite unramified coverings and Galois groups -- Fundamental theorem of Galois theory -- Behavior of primes in coverings -- Frobenius automorphisms -- How to c "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 a |