Ramanujan's theta functions / / by Shaun Cooper
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| Autore: |
Cooper Shaun
|
| Titolo: |
Ramanujan's theta functions / / by Shaun Cooper
|
| Pubblicazione: | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 |
| Edizione: | 1st ed. 2017. |
| Descrizione fisica: | 1 online resource (XVIII, 687 p. 1 illus.) |
| Disciplina: | 512.7 |
| Soggetto topico: | Number theory |
| Geometry, Algebraic | |
| Number Theory | |
| Algebraic Geometry | |
| Nota di bibliografia: | Includes bibliographical references and indexes. |
| Nota di contenuto: | 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. |
| Sommario/riassunto: | 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. |
| Titolo autorizzato: | Ramanujan's Theta Functions |
| ISBN: | 3-319-56172-3 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910254273403321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |