The legacy of Alladi Ramakrishnan in the mathematical sciences
In a distinguished scientific life that had spanned over five decades, Alladi Ramakrishnan made significant contributions to probability and statistics, elementary particle physics, cosmic rays and astrophysics, matrix theory, and the special theory of relativity. Inspired by his visit to the Instit...
| Other Authors: | Alladi, Krishnaswami., Klauder, John R., Rao, C. Radhakrishna 1920-2023., SpringerLink (Online Service) |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
New York :
Springer,
©2010.
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| Physical Description: |
1 online resource (xvii, 575 pages) : illustrations (some color) |
| Subjects: |
Table of Contents:
- Cover13;
- The Legacy of Alladi Ramakrishnan in the Mathematical Sciences
- Preface
- Contents
- Part I The Legacy of Alladi Ramakrishnan
- Contributions of Alladi Ramakrishnan to the Mathematical Sciences
- Alladi Ramakrishnan's Theoretical Physics Seminar
- Telegrams Received for the MATSCIENCE Inauguration
- The Miracle has Happened
- Overseas Trips of Alladi Ramakrishnan
- List of Publications of Alladi Ramakrishnan
- List of PhD Students of Alladi Ramakrishnan
- Part II Pure Mathematics
- Inversion and Invariance of Characteristic Terms: Part I
- 1 Introduction
- 2 Notation
- 3 Remarks and Lemmas
- 4 Newtonian Expansion
- 5 Quadratic Transformations
- 6 Dicritical Divisors
- 7 Field Generators
- 8 Preview of Part II
- 9 Epilogue
- References
- Partitions with Non-Repeating Odd Partsand Q-Hypergeometric Identities
- 1 Introduction
- 2 The Series Expansion
- 3 Sylvester's Identity
- 4 Lebesgue's Identity
- 5 Three Parameter Extension
- 6 The Rogers-Fine Identity
- 7 Partition Interpretations
- References
- q-Catalan Identities
- 1 Introduction
- 2 q-Touchard's Identity
- 3 Koshy's Identity
- 4 Jonah's Identity
- 5 Conclusion
- References
- Completing Brahmagupta's Extension of Ptolemy's Theorem
- 1 Introduction
- 2 Brahmagupta's Refinements of Ptolemy's Theorem
- 3 Further Results of Brahmagupta
- 4 The Third Diagonal of a Cyclic Quadrilateral
- References
- A Transformation Formula Involving the Gamma and Riemann Zeta Functions in Ramanujan's Lost Notebook
- 1 Introduction
- 2 Preliminary Results
- 3 First Proof of Theorem 1.1
- 4 Second Proof of (1.3)
- References
- Ternary Quadratic Forms, Modular Equations, and Certain Positivity Conjectures
- 1 Introduction
- 2 Ramanujan's Modular Equations of Degree 3 and Associated Identities for Ternary Quadratic Forms with Discriminant 144
- 3 Ramanujan's Modular Equations of Degree 5 and Associated Identities for Ternary Quadratic Forms with Discriminant 400
- 4 Ternary Forms with Discriminant 784
- 5 Ternary Forms with Discriminant 3600
- 6 S-Genus
- References
- How Often is n! a Sum of Three Squares?
- 1 Introduction
- 2 The Substitution
- 3 Proof of Theorem 2
- References
- Eulerian Polynomials: From Euler's Time to the Present
- 1 Introduction
- 2 Euler's Definition of the Eulerian Polynomials
- 3 A Formulary for the Eulerian Polynomials
- 4 A Relation with the Tangent Numbers
- 5 The Carlitz q-Eulerian Polynomials
- 6 A Detour to Combinatorics
- References
- Crystal Symmetry Viewed as Zeta Symmetry II
- 1 Introduction
- 2 Lattice Zeta-Function
- 3 Results on Lattice Zeta-Functions
- 4 Applications
- References
- Positive Homogeneous Minima for a System of Linear Forms
- References
- The Divisor Matrix, Dirichlet Series, and SL(2, Z)
- 1 Introduction
- 2 Basic Definitions and Notation
- 3 An Action of SL(2,Z) on Dirichlet Series
- 4 A Jordan Form of the Divisor Matrix
- 5 Construction of Representations
- 6 Proof of Theorem 3.1
- 7 Extending Representations to GL(2,Z)
- 8 Uniqueness of M
- 9 Dirichlet Series in the SL(2,Z)-Orbit of (s)
- 10 The Cubic Equation Relating (s) and (s)
- 11 A Functional Equation for (s)
- References
- Pr.