<電子ブック>
Ramanujan's Theta Functions / by Shaun Cooper
版 | 1st ed. 2017. |
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出版者 | (Cham : Springer International Publishing : Imprint: Springer) |
出版年 | 2017 |
大きさ | XVIII, 687 p. 1 illus : online resource |
著者標目 | *Cooper, Shaun author SpringerLink (Online service) |
件 名 | LCSH:Number theory LCSH:Algebraic geometry FREE:Number Theory FREE:Algebraic Geometry |
一般注記 | Preface -- 0. Sum to Product Identities -- 1. Elliptic Functions -- 2. Transformations -- 3. Theta Functions -- 4. Levels 1, 2, 3, and 4: Jacobi's Inversion Theorem and Ramanujan's Alternative Theories -- 5. Level 5: The Rogers-Ramanujan Continued Fraction -- 6. Level 6: Ramanujan's Cubic Continued Fraction -- 7. Level 7 -- 8. Level 8: The Ramanujan-Gollnitz-Gordon Continued Fraction -- 9. Level 9 -- 10. Level 10: Ramanujan's Function k -- 11. Levels 11 and 23 -- 12. Level 12 -- 13. Hypergeometric Modular Transformations -- 14. Ramanujan's Series for 1/pi -- References Theta functions were studied extensively by Ramanujan. This book provides a systematic development of Ramanujan’s results and extends them to a general theory. The author’s treatment of the subject is comprehensive, providing a detailed study of theta functions and modular forms for levels up to 12. Aimed at advanced undergraduates, graduate students, and researchers, the organization, user-friendly presentation, and rich source of examples, lends this book to serve as a useful reference, a pedagogical tool, and a stimulus for further research. Topics, especially those discussed in the second half of the book, have been the subject of much recent research; many of which are appearing in book form for the first time. Further results are summarized in the numerous exercises at the end of each chapter HTTP:URL=https://doi.org/10.1007/978-3-319-56172-1 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783319561721 |
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EB00200716 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA241-247.5 DC23:512.7 |
書誌ID | 4000116555 |
ISBN | 9783319561721 |
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※2017年9月4日以降