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<図書>
Zeta functions of graphs : a stroll through the garden

責任表示 Audrey Terras
シリーズ Cambridge studies in advanced mathematics ; 128
データ種別 図書
出版者 New York ; Cambridge : Cambridge University Press
出版年 2011
本文言語 英語
大きさ xii, 239 p. : ill. (some col.) ; 24 cm
概要 "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"--続きを見る
目次 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.
電子版へのリンク

所蔵情報

: hbk 理系図1F 開架 031212011000798 413.5/Te 74 2011
: hbk 理系図3F 数理独自 033212010004471 TERR/20/3 2011

書誌詳細

一般注記 Bibliography: p. 230-235
Includes index
著者標目 *Terras, Audrey
件 名 LCSH:Graph theory
LCSH:Functions, Zeta
分 類 LCC:QA166
DC22:511/.5
書誌ID 1001435689
ISBN 9780521113670
NCID BB04063003
巻冊次 : hbk ; ISBN:9780521113670
登録日 2010.12.08
更新日 2017.02.18

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