Bounded Gaps Between Primes: The Epic Breakthroughs of the Early Twenty-First Century

ISBN-13: 9781108836746 / Angielski / Twarda / 2021 / 590 str.

Broughan Kevin Broughan

Opis

A mathematical record of bounded prime gaps breakthroughs, from Erdős to Polymath8, with linked computer programs and complete appendices.

Recenzje

'a wonderful tale of how two lesser-known mathematicians worked extremely hard to solve an intriguing, long-standing open problem that so many leading experts could not.' Sam Chow, London Mathematical Society

Spis treści

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.