Important results surrounding the classic Goldbach conjecture are presented in this book. Beginning with an historical perspective and an overview of essential lemmas and theorems, the discussion further presents a detailed proof of Vinogradov's theorem. The principles of the Hardy–Littlewood circle method are outlined and applied to Goldbach's conjecture. New results by H. Maier and the author utilizing Vinogradov's theorem are proved under the assumption of the generalized Riemann hypothesis. The final chapter lays out an approach to Goldbach's conjecture through theorems by L. G. Schnirelmann; the Appendix features a sketch of H. Helfgott's proof of Goldbach's conjecture offering biographical remarks of mathematicians who have 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 elementary number theory. Additionally, this book will be useful to graduate students and mathematicians in analytic number theory, approximation theory, and to those working on the Goldbach problem.
- ISBN: 978-3-319-57912-2
- Editorial: Springer
- Encuadernacion: Rústica
- Páginas: 121
- Fecha Publicación: 04/09/2017
- Nº Volúmenes: 1
- Idioma: Inglés