Format:
Online-Ressource
,
v.: digital
Edition:
Online-Ausg. Springer eBook Collection. Mathematics and Statistics Electronic reproduction; Available via World Wide Web
ISBN:
1282982656
,
9781441962638
,
9781282982659
Content:
This volume begins with a description of Alladi Ramakrishnan's remarkable scientific career and his grand vision that led to the creation of The Institute of Mathematical Sciences (MATSCIENCE), in Madras (now Chennai), India, in 1962. The lists of his research publications, his PhD students, and other relevant facts relating to his eventful career are included. The inclusion of both research and survey articles by leading mathematicians, statisticians, and physicists who got to know Alladi Ramakrishnan over the years and admired his significant contributions to research and to the scientific profession, have been written and dedicated in this volume to Ramakrishnan's memory.
Note:
Includes bibliographical references
,
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
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4 Newtonian Expansion5 Quadratic Transformations; 6 Dicritical Divisors; 7 Field Generators; 8 Preview of Part II; 9 Epilogue; 9.1 Trigonometry; 9.2 Taylor Expansion and Valuations; 9.3 Discrete Valuation Rings or DVRs; 9.4 Newton Expansion and Hamburger-Noether Expansion; 9.5 Taylor Series with Remainder; 9.6 Polynomials and Power Series; 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
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Referencesq-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
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Ternary Quadratic Forms, Modular Equations, and Certain Positivity Conjectures1 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
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Eulerian Polynomials: From Euler's Time to the Present1 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
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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.
,
Electronic reproduction; Available via World Wide Web
Additional Edition:
ISBN 1282982397
Additional Edition:
ISBN 9781441962621
Language:
English
Subjects:
Mathematics
DOI:
10.1007/978-1-4419-6263-8
URL:
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