This book records in considerable detail the remarkable bounded prime gaps breakthroughs of recent decades, including Polymath8's best result. The material is suitable for graduate students and any mathematician curious about developments in the field. The book is supported by a linked and freely-available package of computer programs.
This book records in considerable detail the remarkable bounded prime gaps breakthroughs of recent decades, including Polymath8's best result. The material is suitable for graduate students and any mathematician curious about developments in the field. The book is supported by a linked and freely-available package of computer programs.
Kevin Broughan is Emeritus Professor at the University of Waikato, New Zealand. He co-founded and is a Fellow of the New Zealand Mathematical Society. Broughan brings a unique set of knowledge and skills to this project, including number theory, analysis, topology, dynamical systems and computational mathematics. He previously authored the two-volume work Equivalents of the Riemann Hypothesis (Cambridge, 2017) and wrote a software package which is part of Goldfeld's Automorphic Forms and L-Functions for the Group GL(n,R) (Cambridge, 2006).
Inhaltsangabe
1. Introduction 2. The sieves of Brun and Selberg 3. Early work 4. The breakthrough of Goldston, Motohashi, Pintz, and Yildirim 5. The astounding result of Yitang Zhang 6. Maynard's radical simplification 7. Polymath's refinements of Maynard's results 8. Variations on Bombieri-Vinogradov 9. Further work and the epilogue Appendix A. Bessel functions of the first kind Appendix B. A type of compact symmetric operator Appendix C. Solving an optimization problem Appendix D. A Brun-Titchmarsh inequality Appendix E. The Weil exponential sum bound Appendix F. Complex function theory Appendix G. The dispersion method of Linnik Appendix H. One thousand admissible tuples Appendix I. PGpack mini-manual References Index.
1. Introduction 2. The sieves of Brun and Selberg 3. Early work 4. The breakthrough of Goldston, Motohashi, Pintz, and Yildirim 5. The astounding result of Yitang Zhang 6. Maynard's radical simplification 7. Polymath's refinements of Maynard's results 8. Variations on Bombieri-Vinogradov 9. Further work and the epilogue Appendix A. Bessel functions of the first kind Appendix B. A type of compact symmetric operator Appendix C. Solving an optimization problem Appendix D. A Brun-Titchmarsh inequality Appendix E. The Weil exponential sum bound Appendix F. Complex function theory Appendix G. The dispersion method of Linnik Appendix H. One thousand admissible tuples Appendix I. PGpack mini-manual References Index.
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