Overview
Features a step-by-step presentation of results of Goldbach's conjecture
Accessible to those that have mastered classical number theory and fundamental notions of mathematical analysis
Equips readers with an extensive bibliography
Includes supplementary material: sn.pub/extras
Includes supplementary material: sn.pub/extras
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Table of contents(4 chapters)
About this book
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.
Reviews
“The monograph is well readable since the author provides many details and thus makes the presentation self-contained. The book will be a valuable addition to every mathematical library. It will serve as an invaluable source to students and professors interested in the subject. It is an important contribution to the mathematical literature.” (Helmut Maier, zbMATH, 2017)
Authors and Affiliations
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Department of Mathematics, ETH Zürich, Zürich, Switzerland
Michael Th. Rassias
Bibliographic Information
Book Title: Goldbach’s Problem
Book Subtitle: Selected Topics
Authors: Michael Th. Rassias
DOI: https://doi.org/10.1007/978-3-319-57914-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Softcover ISBN: 978-3-319-57912-2Published: 07 July 2017
eBook ISBN: 978-3-319-57914-6Published: 25 June 2017
Edition Number: 1
Number of Pages: XV, 122
Topics: Number Theory, Analysis, Numerical Analysis