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＜図書＞
Exponential sums and differential equations
| 責任表示 | by Nicholas M. Katz |
|---|---|
| シリーズ | Annals of mathematics studies ; no. 124 |
| データ種別 | 図書 |
| 出版情報 | Princeton, N.J. : Princeton University Press , 1990 |
| 本文言語 | 英語 |
| 大きさ | ix, 430 p. ; 25 cm |
| 概要 | This book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differential equation... in one complex variable with polynomial coefficients, and the theory of one parameter families of exponential sums over finite fields. After reviewing some results from representation theory, the book discusses results about differential equations and their differential galois groups (G) and one-parameter families of exponential sums and their geometric monodromy groups (G). The final part of the book is devoted to comparison theorems relating G and G of suitably "corresponding" situations, which provide a systematic explanation of the remarkable "coincidences" found "by hand" in the hypergeometric case. This book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differential equations in one complex variable with polynomial coefficients, and the theory of one parameter families of exponential sums over finite fields. After reviewing some results from representation theory, the book discusses results about differential equations and their differential galois groups (G) and one-parameter families of exponential sums and their geometric monodromy groups (G). The final part of the book is devoted to comparison theorems relating G and G of suitably "corresponding" situations, which provide a systematic explanation of the remarkable "coincidences" found "by hand" in the hypergeometric case. 続きを見る |
| 電子版へのリンク | https://hdl.handle.net/2324/6822718 |
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 | KATZ/20/3 | 1990 |
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068222190005730 |
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数理 雑誌室 | SER/AMS/K124 | 1990 |
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068252190009111 |
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書誌詳細
| 一般注記 | Includes bibliographical references (p. 425-430) |
|---|---|
| 著者標目 | *Katz, Nicholas M., 1943- |
| 件 名 | LCSH:Exponential sums LCSH:Differential equations |
| 分 類 | LCC:QA246.7 DC20:512/.73 NDC8:412.3 |
| 書誌ID | 1001054778 |
| ISBN | 0691085986 |
| NCID | BA10962235 |
| 巻冊次 | ISBN:0691085986 ; PRICE:$65.00 : pbk ; ISBN:0691085994 ; PRICE:22.50 |
| 登録日 | 2009.09.17 |
| 更新日 | 2009.11.02 |