Mendeley出力
＜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 |
| 出版情報 | New York ; Cambridge : Cambridge University Press , 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 | https://hdl.handle.net/2324/6831523 |
所蔵情報
| 状態 | 巻次 | 所蔵場所 | 請求記号 | 刷年 | 文庫名称 | 資料番号 | コメント | 予約・取寄 | 複写申込 | 自動書庫 |
|---|---|---|---|---|---|---|---|---|---|---|
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: hbk | 理系図1F 開架 | 413.5/Te 74 | 2011 |
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031212011000798 |
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: hbk | 理系図3F 数理独自 | TERR/20/3 | 2011 |
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033212010004471 |
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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 |