The Legacy of Alladi Ramakrishnan in the Mathematical Sciences

1. Front Matter

   Pages i-xvii

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2. The Legacy of Alladi Ramakrishnan

   1. Front Matter

      Pages 1-1

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   2. Contributions of Alladi Ramakrishnan to the Mathematical Sciences

      • Krishnaswami Alladi

      Pages 3-9

   3. Alladi Ramakrishnan’s Theoretical Physics Seminar

      • Krishnaswami Alladi

      Pages 11-24

   4. Telegrams Received for the MATSCIENCE Inauguration

      • Krishnaswami Alladi

      Pages 25-65

   5. The Miracle has Happened

      • Alladi Ramakrishnan

      Pages 67-71

   6. Overseas Trips of Alladi Ramakrishnan

      • Krishnaswami Alladi

      Pages 73-80

   7. List of Publications of Alladi Ramakrishnan

      • Krishnaswami Alladi, John R. Klauder, Calyampudi R. Rao

      Pages 81-87

   8. List of PhD Students of Alladi Ramakrishnan

      • Krishnaswami Alladi, John R. Klauder, Calyampudi R. Rao

      Pages 89-89

3. Pure Mathematics

   1. Front Matter

      Pages 91-91

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   2. Inversion and Invariance of Characteristic Terms: Part I

      • Shreeram S. Abhyankar

      Pages 93-168

   3. Partitions with Non-Repeating Odd Parts and Q-Hypergeometric Identities

      • Krishnaswami Alladi

      Pages 169-182

   4. q-Catalan Identities

      • George E. Andrews

      Pages 183-190

   5. Completing Brahmagupta’s Extension of Ptolemy’s Theorem

      • Richard Askey

      Pages 191-197

   6. A Transformation Formula Involving the Gamma and Riemann Zeta Functions in Ramanujan’s Lost Notebook

      • Bruce C. Berndt, Atul Dixit

      Pages 199-210

   7. Ternary Quadratic Forms, Modular Equations, and Certain Positivity Conjectures

      • Alexander Berkovich, William C. Jagy

      Pages 211-241

   8. How Often is n! a Sum of Three Squares?

      • Jean-Marc Deshouillers, Florian Luca

      Pages 243-251

   9. Eulerian Polynomials: From Euler’s Time to the Present

      • Dominique Foata

      Pages 253-273

   10. Crystal Symmetry Viewed as Zeta Symmetry II

       • Shigeru Kanemitsu, Haruo Tsukada

       Pages 275-292

   11. Positive Homogeneous Minima for a System of Linear Forms

       • Srinivasacharya Raghavan

       Pages 293-297

Alladi Ramakrishnan (1923–2008) was an eminent scientist who had a wide range of research interests in theoretical and mathematical physics. Professor Ramakrishnan made signi?cant contributions to probability and statistics, elem- tary particle physics, cosmic rays and astrophysics, matrix theory, and the special theory of relativity. Ramakrishnan believedstrongly that in addition to doing fun- mental research, one must contribute to the advancementof the profession. Inspired by his visit to the Institute for Advanced Study in Princeton in 1957–1958, he returned to Madras and began the Theoretical Physics Seminar at his family home Ekamra Nivas. These seminars were ultimately responsible for the creation of MATSCIENCE, The Institute of Mathematical Sciences in 1962. This institute, of which he was the Director for its ?rst 21years, has grown steadily in size and stature, and is his monumental contribution to the profession. In a distinguished scienti?c life that has spanned more than ?ve decades, Professor Ramakrishnan has come into close contact with, and was in?uenced by, several eminent mathema- cians and physicists, and has moulded the careers of his several students and young researchers. This volume, which is a tribute to his great legacy, not only deals with his signi?cant contributions to research and the profession, but also contains a ?ne collection of research and survey papers by leading physicists and mathematicians that cover a broad range of areas in the mathematical sciences.

• Algebra
• Alladi Ramakrishnan memorial
• MATSCIENCE
• Permutation
• Quark
• astrophysics
• cosmic rays
• elementary particles
• mathematical physics
• matrix theory
• number theory
• probability
• statistics
• theoretical physics

• , Department of Mathematics, University of Florida, Gainesville, USA

  Krishnaswami Alladi

• , Department of Physics, University of Florida, Gainesville, USA

  John R. Klauder

• , Department of Statistics, The Pennsylvania State University, University Park, USA

  Calyampudi R. Rao

Krishnaswami Alladi is the editor in Chief of Springer's Ramanujan Journal, and the Development in Mathematics Book series. He was chair of the mathematics department of the University of Florida. In addition to his contributions of bibliographic material about his father, Krishnaswami Alladi has directed and organized the development of this tribute volume. C.R. Rao is inarguably the most prominent academic in the field of Statistics in current times. John Klauder has served on the Physics Advisory Panel of the NSF and been Editor of the Journal of Mathematical Physics, and as President of the International Association of Mathematical Physics.

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