Details

Ramanujan's Theta Functions


Ramanujan's Theta Functions



von: Shaun Cooper

130,89 €

Verlag: Springer
Format: PDF
Veröffentl.: 12.06.2017
ISBN/EAN: 9783319561721
Sprache: englisch

DRM-geschütztes eBook, Sie benötigen z.B. Adobe Digital Editions und eine Adobe ID zum Lesen.

Beschreibungen

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.
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.
Shaun Cooper received a PhD in Mathematics from the University of Wisconsin at Madison in 1995 and has worked at Massey University in New Zealand ever since. He was a visiting Assistant Professor at the University of Minnesota for one semester in 2000, and has spent 12 months each at the National University of Singapore (2007/8) and the University of Newcastle, Australia (2015/16). He is the author of approximately 70 refereed journal articles and edited the book Development of Elliptic Functions According to Ramanujan.
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.
Contains a detailed and systematic analysis of theta functions, by level and by weightServes as a useful, encyclopedic reference, designed to be a full and comprehensive study of select levels of Theta functions and modular formsFeatures topics that have been the subject of much recent research, with the material organized into a systematic settingMarks the first time many of the topics within will have appeared in book form

Diese Produkte könnten Sie auch interessieren:

Engineering Biostatistics
Engineering Biostatistics
von: Brani Vidakovic
PDF ebook
104,99 €
Measuring Agreement
Measuring Agreement
von: Pankaj K. Choudhary, Haikady N. Nagaraja
PDF ebook
99,99 €
Challenges in Mechanics of Time Dependent Materials, Volume 2
Challenges in Mechanics of Time Dependent Materials, Volume 2
von: Alex Arzoumanidis, Meredith Silberstein, Alireza Amirkhizi
PDF ebook
178,49 €