In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated, "Ramanujan's lost notebook." Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony.
This fifth and final installment of the authors’ examination of Ramanujan’s lost notebook focuses on the mock theta functions first introduced in Ramanujan’s famous Last Letter. This volume proves all of the assertions about mock theta functions in the lost notebook and in the Last Letter, particularly the celebrated mock theta conjectures. Other topics feature Ramanujan’s many elegant Euler products and the remaining entries on continued fractions not discussed in the preceding volumes.
Review from the second volume:"Fans of Ramanujan's mathematics are sure to be delighted by this book. While some of the content is taken directly from published papers, most chapters contain new material and some previously published proofs have been improved. Many entries are just begging for further study and will undoubtedly be inspiring research for decades to come. The next installment in this series is eagerly awaited."- MathSciNet
Review from the first volume:"Andrews and Berndt are to be congratulated on the job they are doing. This is the first step...on the way to an understanding of the work of the genius Ramanujan. It should act as an inspiration to future generations of mathematicians to tackle a job that will never be complete."- Gazette of the Australian Mathematical Society
Author(s): George E. Andrews, Bruce C. Berndt
Edition: 1
Publisher: Springer
Year: 2018
Language: English
Pages: 433
Front Matter ....Pages i-xii
Introduction (George E. Andrews, Bruce C. Berndt)....Pages 1-4
Third Order Mock Theta Functions: Elementary Identities (George E. Andrews, Bruce C. Berndt)....Pages 5-16
Fifth Order Mock Theta Functions: Elementary Identities (George E. Andrews, Bruce C. Berndt)....Pages 17-33
Third Order Mock Theta Functions: Partial Fraction Expansions (George E. Andrews, Bruce C. Berndt)....Pages 35-58
The Mock Theta Conjectures: Equivalence (George E. Andrews, Bruce C. Berndt)....Pages 59-76
Fifth Order Mock Theta Functions: Proof of the Mock Theta Conjectures (George E. Andrews, Bruce C. Berndt)....Pages 77-108
Sixth Order Mock Theta Functions (George E. Andrews, Bruce C. Berndt)....Pages 109-147
Tenth Order Mock Theta Functions: Part I, The First Four Identities (George E. Andrews, Bruce C. Berndt)....Pages 149-183
Tenth Order Mock Theta Functions: Part II, Identities for ϕ10(q), ψ10(q) (George E. Andrews, Bruce C. Berndt)....Pages 185-205
Tenth Order Mock Theta Functions: Part III, Identities for χ10(q), X10(q) (George E. Andrews, Bruce C. Berndt)....Pages 207-228
Tenth Order Mock Theta Functions: Part IV (George E. Andrews, Bruce C. Berndt)....Pages 229-248
Transformation Formulas: 10th Order Mock Theta Functions (George E. Andrews, Bruce C. Berndt)....Pages 249-290
Two Identities Involving a Mordell Integral and Appell–Lerch Sums (George E. Andrews, Bruce C. Berndt)....Pages 291-309
Ramanujan’s Last Letter to Hardy (George E. Andrews, Bruce C. Berndt)....Pages 311-320
Euler Products in Ramanujan’s Lost Notebook (George E. Andrews, Bruce C. Berndt)....Pages 321-356
Continued Fractions (George E. Andrews, Bruce C. Berndt)....Pages 357-363
Recent Work on Mock Theta Functions (George E. Andrews, Bruce C. Berndt)....Pages 365-372
Commentary on and Corrections to the First Four Volumes (George E. Andrews, Bruce C. Berndt)....Pages 373-388
The Continuing Mystery (George E. Andrews, Bruce C. Berndt)....Pages 389-401
Back Matter ....Pages 403-430
