About this product

Product Identifiers

PublisherSpringer International Publishing A&G

ISBN-103319561715

ISBN-139783319561714

eBay Product ID (ePID)234402573

Product Key Features

Number of PagesXviii, 687 Pages

Publication NameRamanujan's Theta Functions

LanguageEnglish

SubjectFunctional Analysis, Number Theory, Geometry / Algebraic

Publication Year2017

TypeTextbook

AuthorShaun Cooper

Subject AreaMathematics

FormatHardcover

Dimensions

Item Weight43 Oz

Item Length9.3 in

Item Width6.1 in

Additional Product Features

Reviews"Each chapter contains an extensive set of exercises, making the book suitable for students interested in an introduction to q-series, elliptic functions, and modular forms without necessarily requiring the theory of modular forms as a prerequisite. ... it will be a valuable reference book on Ramanujan's theta function identities together with their modern extensions and applications." (Jeremy Lovejoy, Mathematical Reviews, April, 2018) "This is a big and bountiful book, clearly written as a labor of love, and well worth the effort (both of writing and reading it). The book is pitched at advanced undergraduates, graduate students, and professionals or researchers, and this is entirely consonant with this kind of number theory ... . It's been a long time since I visited this material, but I am very happy to see it again." (Michael Berg, MAA Reviews, November, 2017), "This is a big and bountiful book, clearly written as a labor of love, and well worth the effort (both of writing and reading it). The book is pitched at advanced undergraduates, graduate students, and professionals or researchers, and this is entirely consonant with this kind of number theory ... . It's been a long time since I visited this material, but I am very happy to see it again." (Michael Berg, MAA Reviews, November, 2017)

Dewey Edition23

Number of Volumes1 vol.

IllustratedYes

Dewey Decimal515.984

Table Of ContentPreface.- 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.

SynopsisTheta 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.

LC Classification NumberQA241-247.5