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  • BTU Cottbus  (15)
  • SB Luckenwalde
  • TH Wildau
  • Kreisbibliothek des Landkreises Spree-Neiße
  • GB Schipkau
  • SB Putlitz
  • SB Wittenberge
  • Berndt, Bruce C.  (15)
  • 1
    UID:
    b3kat_BV040348498
    Umfang: 1 Online-Ressource
    ISBN: 9781461438090 , 9781461438106
    In: 3
    Sprache: Englisch
    Mehr zum Autor: Berndt, Bruce C. 1939-
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  • 2
    UID:
    b3kat_BV040348532
    Umfang: 1 Online-Ressource
    ISBN: 9780387777658 , 9780387777665
    In: 2
    Sprache: Englisch
    Mehr zum Autor: Berndt, Bruce C. 1939-
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  • 3
    UID:
    b3kat_BV040348510
    Umfang: 1 Online-Ressource
    ISBN: 9780387255293 , 9780387281247
    In: 1
    Sprache: Englisch
    Mehr zum Autor: Berndt, Bruce C. 1939-
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  • 4
    UID:
    b3kat_BV041215025
    Umfang: 1 Online-Ressource
    ISBN: 9781461440802 , 9781461440819
    In: 4
    Sprache: Englisch
    Mehr zum Autor: Berndt, Bruce C. 1939-
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  • 5
    UID:
    b3kat_BV045899441
    Umfang: 1 Online-Ressource (XII, 430 Seiten, 3 illus., 1 illus. in color)
    ISBN: 9783319778341
    In: 5
    Weitere Ausg.: Erscheint auch als Druck-Ausgabe ISBN 978-3-319-77832-7
    Weitere Ausg.: Erscheint auch als Druck-Ausgabe ISBN 978-3-319-77833-4
    Sprache: Englisch
    Fachgebiete: Mathematik
    RVK:
    Schlagwort(e): Ramanujan Aiyangar, Srinivasa 1887-1920 ; Thetafunktion
    URL: Volltext  (URL des Erstveröffentlichers)
    Mehr zum Autor: Berndt, Bruce C. 1939-
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  • 6
    UID:
    almahu_9947362831302882
    Umfang: VIII, 560 p. , online resource.
    ISBN: 9781461234647
    Serie: Progress in Mathematics ; 85
    Inhalt: On April 25-27, 1989, over a hundred mathematicians, including eleven from abroad, gathered at the University of Illinois Conference Center at Allerton Park for a major conference on analytic number theory. The occa­ sion marked the seventieth birthday and impending (official) retirement of Paul T. Bateman, a prominent number theorist and member of the mathe­ matics faculty at the University of Illinois for almost forty years. For fifteen of these years, he served as head of the mathematics department. The conference featured a total of fifty-four talks, including ten in­ vited lectures by H. Delange, P. Erdos, H. Iwaniec, M. Knopp, M. Mendes France, H. L. Montgomery, C. Pomerance, W. Schmidt, H. Stark, and R. C. Vaughan. This volume represents the contents of thirty of these talks as well as two further contributions. The papers span a wide range of topics in number theory, with a majority in analytic number theory.
    Anmerkung: q-Trinomial Coefficients and Rogers-Ramanujan Identities -- Evaluations of Selberg Character Sums -- Oscillations of Quadratic L-Functions -- Elementary Proof of a Theorem of Bateman -- The Prime k-Tuplets Conjecture on Average -- On Arithmetic Functions Involving Consecutive Divisors -- Small Zeros of Quadratic Forms Modulo p, II -- Zeros of Derivatives of the Riemann Zeta-Function near the Critical Line -- On some Exponential Sums -- On the Integers n for which ?(n) = k -- A Boundary Problem for a Pair of Differential-Delay Equations related to Sieve Theory, I -- Some Remarks about Multiplicative Functions of Modulus 〈 1 -- On the Normal Behavior of the Iterates of some Arithmetic Functions -- On the Number ofPartitions of n without a Given Subsum, II -- On Gaps between SquarefreeNumbers -- Some Arithmetical Semigroups -- Norms in Arithmetic Progressions -- Lower Bounds for Least Quadratic Non-Residues -- Some Conjectures in Analytic Number Theory and their Connection with Fermat’s Last Theorem -- Modular Integrals and their Mellin Transforms -- A Congruence for Generalized Frobenius Partitions with 3 Colors Modulo Powers of 3 -- The Coefficients of Cyclotomic Polynomials -- The Rudin-Shapiro Sequence, Ising Chain, and Paperfolding -- On Binomial Equations over Function Fields and a Conjecture of Siegel -- Best Possible Results on the Density of Sumsets -- Some Powers of the Euler Product -- A Divergent Argument Concerning Hadamard Roots of Rational Functions -- Diagonalizing Eisenstein Series. I -- Some Binary Partition Functions -- On the Minimal Level of Modular Forms -- Inequalities for Heights of Algebraic Subspaces and the Thue-Siegel Principle -- The Abstract Prime Number Theorem for Algebraic Function Fields.
    In: Springer eBooks
    Weitere Ausg.: Printed edition: ISBN 9780817634810
    Sprache: Englisch
    Schlagwort(e): Festschrift ; Konferenzschrift ; Konferenzschrift
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  • 7
    Online-Ressource
    Online-Ressource
    New York, NY :Springer New York,
    UID:
    almahu_9947362988302882
    Umfang: XII, 360 p. , online resource.
    ISBN: 9781461245308
    Inhalt: During the years 1903-1914, Ramanujan recorded many of his mathematical discoveries in notebooks without providing proofs. Although many of his results were already in the literature, more were not. Almost a decade after Ramanujan's death in 1920, G.N. Watson and B.M. Wilson began to edit his notebooks but never completed the task. A photostat edition, with no editing, was published by the Tata Institute of Fundamental Research in Bombay in 1957. This book is the second of four volumes devoted to the editing of Ramanujan's Notebooks. Part I, published in 1985, contains an account of Chapters 1-9 in the second notebook as well as a description of Ramanujan's quarterly reports. In this volume, we examine Chapters 10-15 in Ramanujan's second notebook. If a result is known, we provide references in the literature where proofs may be found; if a result is not known, we attempt to prove it. Not only are the results fascinating, but, for the most part, Ramanujan's methods remain a mystery. Much work still needs to be done. We hope readers will strive to discover Ramanujan's thoughts and further develop his beautiful ideas.
    Anmerkung: 10 Hypergeometric Series, I -- 11 Hypergeometric Series, II -- 12 Continued Fractions -- 13 Integrals and Asymptotic Expansions -- 14 Infinite Series -- 15 Asymptotic Expansions and Modular Forms -- References.
    In: Springer eBooks
    Weitere Ausg.: Printed edition: ISBN 9781461288657
    Sprache: Englisch
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  • 8
    Online-Ressource
    Online-Ressource
    New York, NY :Springer New York :
    UID:
    almahu_9947363002202882
    Umfang: XIII, 510 p. , online resource.
    ISBN: 9781461209652
    Inhalt: During the time period between 1903 and 1914, Ramanujan worked in almost complete isolation in India. Throughout these years, he recorded his mathematical results without proofs in notebooks. Upon Ramanujan's death in 1920, G.H. Hardy strongly urged that Ramanujan's notebooks be published and edited. The English mathematicians G.N. Watson and B.M. Wilson began this task in 1929, but although they devoted nearly ten years to the project, the work was never completed. In 1957, the Tata Institute of Fundamental Research in Bombay published a photostat edition of the notebooks, but no editing was undertaken. In 1977, Berndt began the tasks of editing Ramanujan's notebooks. Proofs are provided to theorems not yet proven in previous literature, and many results are so startling and different that there are no results akin to them in the literature.
    Anmerkung: 16 q-Series and Theta-Functions -- 17 Fundamental Properties of Elliptic Functions -- 18 The Jacobian Elliptic Functions -- 19 Modular Equations of Degrees 3, 5, and 7 and Associated Theta-Function Identities -- 20 Modular Equations of Higher and Composite Degrees -- 21 Eisenstein Series -- References.
    In: Springer eBooks
    Weitere Ausg.: Printed edition: ISBN 9781461269632
    Sprache: Englisch
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  • 9
    UID:
    almahu_9947363175402882
    Umfang: XVI, 314 p. , online resource.
    ISBN: 9783034882231
    Serie: Trends in Mathematics
    Inhalt: To mark the World Mathematical Year 2000 an International Conference on Number Theory and Discrete Mathematics in honour of the legendary Indian Mathematician Srinivasa Ramanuj~ was held at the centre for Advanced study in Mathematics, Panjab University, Chandigarh, India during October 2-6, 2000. This volume contains the proceedings of that conference. In all there were 82 participants including 14 overseas participants from Austria, France, Hungary, Italy, Japan, Korea, Singapore and the USA. The conference was inaugurated by Prof. K. N. Pathak, Hon. Vice-Chancellor, Panjab University, Chandigarh on October 2, 2000. Prof. Bruce C. Berndt of the University of Illinois, Urbana­ Chaimpaign, USA delivered the key note address entitled "The Life, Notebooks and Mathematical Contributions of Srinivasa Ramanujan". He described Ramanujan--as one of this century's most influential Mathematicians. Quoting Mark K. ac, Prof. George E. Andrews of the Pennsylvania State University, USA, in his message for the conference, described Ramanujan as a "magical genius". During the 5-day deliberations invited speakers gave talks on various topics in number theory and discrete mathematics. We mention here a few of them just as a sampling: • M. Waldschmidt, in his article, provides a very nice introduction to the topic of multiple poly logarithms and their special values. • C.
    Anmerkung: Multiple Polylogarithms: An Introduction -- A (Conjectural) 1/3-phenomenon for the Number of Rhombus Tilings of a Hexagon which contain a Fixed Rhombus -- The Influence of Carr’s Synopsis on Ramanujan -- A Bailey Lemma from the Quintuple Product -- Little Flowers to G.H. Hardy (07-02-1877-01-12-1947) -- Rogers-Ramanujan Type Identities for Burge’s Restricted Partition Pairs Via Restricted Frobenius Partitions -- On q-additive and q-multiplicative Functions -- Antimagic Labeling of Complete m-ary Trees -- Some Recent Advances on Symmetric, Quasi-Symmetric and Quasi-Multiple Designs -- On T-core Partitions and Quadratic Forms -- Observations on Some Algebraic Equations Associated with Ramanujan’s Work -- On Rapidly Convergent Series for Dirichlet L-function Values Via the Modular Relation -- On a Conjecture of Andrews-II -- Integrity of P2× Pn -- A Note on Cordial Labelings of Multiple Shells -- A Report on Additive Complements of the Squares -- Transcendental Infinite Sums and Some Related Questions -- The Lehmer Problem on the Euler Totient: A Pendora’s Box of Unsolvable Problems -- The Problems Solved by Ramanujan in the Journal of the Indian Mathematical Society -- On the gcd and Icm of Matrices Over Dedekind Domains -- The Billiard Ball Motion Problem I: A Markoff Type Chain for the Octahedron in $${{\Re }^{3}}$$ -- Hilbert’s Seventeenth Problem and Pfister’s Work on Quadratic Forms -- Certain Representations of Mock-Theta Functions -- Bi-Graceful Graphs -- Wheels, Cages and Cubes -- Relevance of Srinivasa Ramanujan at the Dawn of the New Millennium -- Number of Solutions of Equations over Finite Fields and a Conjecture of Lang and Weil -- On An Additive Question -- n-Colour Partitions.
    In: Springer eBooks
    Weitere Ausg.: Printed edition: ISBN 9783034894814
    Sprache: Englisch
    Schlagwort(e): Konferenzschrift
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  • 10
    Online-Ressource
    Online-Ressource
    New York, NY :Springer New York :
    UID:
    almahu_9947362999602882
    Umfang: XIII, 624 p. , online resource.
    ISBN: 9781461216247
    Inhalt: During the years 1903-1914, Ramanujan recorded most of his mathematical dis­ coveries without proofs in notebooks. Although many of his results had already been published by others, most had not. Almost a decade after Ramanujan's death in 1920, G. N. Watson and B. M. Wilson began to edit Ramanujan's notebooks, but, despite devoting over ten years to this project, they never completed their task. An unedited photostat edition of the notebooks was published by the Tata Institute of Fundamental Research in Bombay in 1957. This book is the fifth and final volume devoted to the editing of Ramanujan's notebooks. Parts I-III, published, respectively, in 1985, 1989, and 1991, contain accounts of Chapters 1-21 in the second notebook, a revised enlarged edition of the first. Part IV, published in 1994, contains results from the 100 unorganized pages in the second notebook and the 33 unorganized pages comprising the third notebook. Also examined in Part IV are the 16 organized chapters in the first notebook, which contain very little that is not found in the second notebook. In this fifth volume, we examine the remaining contents from the 133 unorganized pages in the second and third notebooks, and the claims in the 198 unorganized pages of the first notebook that cannot be found in the succeeding notebooks.
    Anmerkung: 32 Continued Fractions -- 1 The Rogers—Ramanujan Continued Fraction -- 2 Other q—Continued Fractions -- 3 Continued Fractions Arising from Products of Gamma Functions -- 4 Other Continued Fractions -- 5 General Theorems -- 33 Ramanujan’s Theories of Elliptic Functions to Alternative Bases -- 1 Introduction -- 2 Ramanujan’s Cubic Transformation, the Borweins’ Cubic Theta—Function Identity, and the Inversion Formula -- 3 The Principles of Triplication and Trimidiation -- 4 The Eisenstein Series L, M, and N -- 5 A Hypergeometric Transformation and Associated Transfer Principle -- 6 More Higher Order Transformations for Hypergeometric Series -- 7 Modular Equations in the Theory of Signature 3 -- 8 The Inversion of an Analogue of K (k) in Signature 3 -- 9 The Theory for Signature 4 -- 10 Modular Equations in the Theory of Signature 4 -- 11 The Theory for Signature 6 -- 12 An Identity from the First Notebook and Further Hypergeometric Transformations -- 13 Some Enigmatic Formulas Near the End of the Third Notebook -- 14 Concluding Remarks -- 34 Class Invariants and Singular Moduli -- 1 Introduction -- 2 Table of Class Invariants -- 3 Computation of Gnand gnwhen 9/n -- 4 Kronecker’s Limit Formula and General Formulas for Class Invariants -- 5 Class Invariants Via Kronecker’s Limit Formula -- 6 Class Invariants Via Modular Equations -- 7 Class Invariants Via Class Field Theory -- 8 Miscellaneous Results -- 9 Singular Moduli -- 10 A Certain Rational Function of Singular Moduli -- 11 The Modular j-invariant -- 35 Values of Theta-Functions -- 0 Introduction -- 1 Elementary Values -- 2 Nonelementary Values of -- 3 A Remarkable Product of Theta-Functions -- 36 Modular Equations and Theta-Function Identities in Notebook 1 -- 1 Modular Equations of Degree 3 and Related Theta-Function Identities -- 2 Modular Equations of Degree 5 and Related Theta-Function Identities -- 3 Other Modular Equations and Related Theta-Function Identities -- 4 Identities Involving Lambert Series -- 5 Identities Involving Eisenstein Series -- 6 Modular Equations in the Form of Schläfli -- 7 Modular Equations in the Form of Russell -- 8 Modular Equations in the Form of Weber -- 9 Series Transformations Associated with Theta-Functions -- 10 Miscellaneous Results -- 37 Infinite Series -- 38 Approximations and Asymptotic Expansions -- 39 Miscellaneous Results in the First Notebook -- Location of Entries in the Unorganized Portions of Ramanujan’s First Notebook -- References.
    In: Springer eBooks
    Weitere Ausg.: Printed edition: ISBN 9781461272212
    Sprache: Englisch
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