Mendeley出力
＜図書＞
An introduction to G-functions
| 責任表示 | by Bernard Dwork, Giovanni Gerotto, and Francis J. Sullivan |
|---|---|
| シリーズ | Annals of mathematics studies ; no. 133 |
| データ種別 | 図書 |
| 出版情報 | Princeton, N.J. : Princeton University Press , 1994 |
| 本文言語 | 英語 |
| 大きさ | xxi, 323 p. : ill. ; 25 cm |
| 概要 | Written for advanced undergraduate and first-year graduate students, this book aims to introduce students to a serious level of p-adic analysis with important implications for number theory. The main ...bject is the study of G-series, that is, power series y=aij=0 Ajxj with coefficients in an algebraic number field K. These series satisfy a linear differential equation Ly=0 with LIK(x) [d/dx] and have non- zero radii of convergence for each imbedding of K into the complex numbers. They have the further property that the common denominators of the first s coefficients go to infinity geometrically with the index s. After presenting a review of valuation theory and elementary p-adic analysis together with an application to the congruence zeta function, this book offers a detailed study of the p-adic properties of formal power series solutions of linear differential equations. In particular, the p-adic radii of convergence and the p-adic growth of coefficients are studied. Recent work of Christol, Bombieri, Andre, and Dwork is treated and augmented. The book concludes with Chudnovsky's theorem: the analytic continuation of a G- series is again a G-series. This book will be indispensable for those wishing to study the work of Bombieri and Andre on global relations and for the study of the arithmetic properties of solutions of ordinary differential equations. Written for advanced undergraduate and first-year graduate students, this book aims to introduce students to a serious level of p-adic analysis with important implications for number theory. The main object is the study of G-series, that is, power series y=aij=0 Ajxj with coefficients in an algebraic number field K. These series satisfy a linear differential equation Ly=0 with LIK(x) [d/dx] and have non- zero radii of convergence for each imbedding of K into the complex numbers. They have the further property that the common denominators of the first s coefficients go to infinity geometrically with the index s. After presenting a review of valuation theory and elementary p-adic analysis together with an application to the congruence zeta function, this book offers a detailed study of the p-adic properties of formal power series solutions of linear differential equations. In particular, the p-adic radii of convergence and the p-adic growth of coefficients are studied. Recent work of Christol, Bombieri, Andre, and Dwork is treated and augmented. The book concludes with Chudnovsky's theorem: the analytic continuation of a G- series is again a G-series. This book will be indispensable for those wishing to study the work of Bombieri and Andre on global relations and for the study of the arithmetic properties of solutions of ordinary differential equations. 続きを見る |
| 電子版へのリンク | https://hdl.handle.net/2324/6822641 |
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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理系図3F 数理独自 | DWOR/10/2 | 1994 |
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068222194004097 |
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書誌詳細
| 一般注記 | On t.p. "G" is italicized Includes bibliography (p. 317-319) and index |
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| 著者標目 | *Dwork, Bernard M Gerotto, Giovanni Sullivan, Francis Joseph |
| 件 名 | LCSH:H-functions LCSH:p-adic analysis |
| 分 類 | LCC:QA242.5 DC20:515/.55 NDC8:413.5 |
| 書誌ID | 1000038122 |
| ISBN | 0691036756 |
| NCID | BA23000207 |
| 巻冊次 | ISBN:0691036756 ; PRICE:$59.50 : pbk ; ISBN:0691036810 ; PRICE:$29.95 |
| 登録日 | 2009.09.10 |
| 更新日 | 2009.11.02 |