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Goldbach's problem [electronic resource] : selected topics

Goldbach's problem [electronic resource] : selected topics

Material type
E-Book(소장)
Personal Author
Rassias, Michael Th., 1987-.
Title Statement
Goldbach's problem [electronic resource] : selected topics / Michael Th. Rassias.
Publication, Distribution, etc
Cham :   Springer,   c2017.  
Physical Medium
1 online resource (xv, 122 p.).
ISBN
9783319579146 (e-book) 9783319579122
요약
Important results surrounding the proof of Goldbach's ternary conjecture are presented in this book. Beginning with an historical perspective along with an overview of essential lemmas and theorems, this monograph moves on to a detailed proof of Vinogradov's theorem. The principles of the Hardy-Littlewood circle method are outlined and applied to Goldbach's ternary conjecture. New results due to H. Maier and the author on Vinogradov's theorem are proved under the assumption of the Riemann hypothesis. The final chapter discusses an approach to Goldbach's conjecture through theorems by L. G. Schnirelmann. This book concludes with an Appendix featuring a sketch of H. Helfgott's proof of Goldbach's ternary conjecture. The Appendix also presents some biographical remarks of mathematicians whose research has played a seminal role on the Goldbach ternary problem.  The author's step-by-step approach makes this book accessible to those that have mastered classical number theory and fundamental notions of mathematical analysis. This book will be particularly useful to graduate students and mathematicians in analytic number theory, approximation theory as well as to researchers working on Goldbach's problem.
General Note
Title from e-Book title page.  
Content Notes
Foreword -- 1. Introduction -- 2. Step by step proof of Vinogradov's theorem -- The ternary Goldbach problem with a prime and two isolated primes -- 4.  Basic steps of the proof of Schnirelmann's theorem. - Appendix. - Index. -Bibliography.
Bibliography, Etc. Note
Includes bibliographical references and index.
이용가능한 다른형태자료
Issued also as a book.  
Subject Added Entry-Topical Term
Goldbach conjecture. Numbers, Prime. Number theory.
Short cut
URL
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001 000046011671
005 20200110160424
006 m d
007 cr
008 200107s2017 sz ob 001 0 eng d
020 ▼a 9783319579146 (e-book)
020 ▼a 9783319579122
040 ▼a 211009 ▼c 211009 ▼d 211009
050 4 ▼a QA241-247.5
082 0 4 ▼a 512.7 ▼2 23
084 ▼a 512.7 ▼2 DDCK
090 ▼a 512.7
100 1 ▼a Rassias, Michael Th., ▼d 1987-.
245 1 0 ▼a Goldbach's problem ▼h [electronic resource] : ▼b selected topics / ▼c Michael Th. Rassias.
260 ▼a Cham : ▼b Springer, ▼c c2017.
300 ▼a 1 online resource (xv, 122 p.).
500 ▼a Title from e-Book title page.
504 ▼a Includes bibliographical references and index.
505 0 ▼a Foreword -- 1. Introduction -- 2. Step by step proof of Vinogradov's theorem -- The ternary Goldbach problem with a prime and two isolated primes -- 4.  Basic steps of the proof of Schnirelmann's theorem. - Appendix. - Index. -Bibliography.
520 ▼a Important results surrounding the proof of Goldbach's ternary conjecture are presented in this book. Beginning with an historical perspective along with an overview of essential lemmas and theorems, this monograph moves on to a detailed proof of Vinogradov's theorem. The principles of the Hardy-Littlewood circle method are outlined and applied to Goldbach's ternary conjecture. New results due to H. Maier and the author on Vinogradov's theorem are proved under the assumption of the Riemann hypothesis. The final chapter discusses an approach to Goldbach's conjecture through theorems by L. G. Schnirelmann. This book concludes with an Appendix featuring a sketch of H. Helfgott's proof of Goldbach's ternary conjecture. The Appendix also presents some biographical remarks of mathematicians whose research has played a seminal role on the Goldbach ternary problem.  The author's step-by-step approach makes this book accessible to those that have mastered classical number theory and fundamental notions of mathematical analysis. This book will be particularly useful to graduate students and mathematicians in analytic number theory, approximation theory as well as to researchers working on Goldbach's problem.
530 ▼a Issued also as a book.
538 ▼a Mode of access: World Wide Web.
650 0 ▼a Goldbach conjecture.
650 0 ▼a Numbers, Prime.
650 0 ▼a Number theory.
856 4 0 ▼u https://oca.korea.ac.kr/link.n2s?url=https://doi.org/10.1007/978-3-319-57914-6
945 ▼a KLPA
991 ▼a E-Book(소장)

Holdings Information

No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Main Library/e-Book Collection/ Call Number CR 512.7 Accession No. E14018612 Availability Loan can not(reference room) Due Date Make a Reservation Service M

Contents information

Table of Contents

CONTENTS
Introduction = 1
1 Results Towards the Proof of the Ternary Goldbach Conjecture (TGC) = 2
2 Results Towards a Proof of the Binary Goldbach Conjecture (BGC) = 3
Step-by-Step Proof of Vinogradov''''s Theorem = 7
 1 Introductory Lemmas and Theorems = 7
 2 The Circle Method = 31
 3 Proof of Vinogradov''''s Theorem = 33
  3.1 The Contribution of the Major Arcs = 36
  3.2 The Contribution of the Minor Arcs = 48
  3.3 Putting It All Together = 63
The Ternary Goldbach Problem with a Prime and Two Isolated Primes = 67
 1 Introduction = 69
 2 Construction of the Isolated Residue Class = 69
 3 The Circle Method = 77
 4 Conclusion = 86
Basic Steps of the Proof of Schnirelmann''''s Theorem = 87
Appendix = 99
For Further Reading = 113
Bibliography = 117
Index = 121

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