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Bounded Gaps Between Primes : The Epic Breakthroughs of the Early Twenty-First Century by Kevin Broughan (2021, Trade Paperback)
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About this product
Product Identifiers
PublisherCambridge University Press
ISBN-101108799205
ISBN-139781108799201
eBay Product ID (ePID)5050087169
Product Key Features
Number of Pages590 Pages
LanguageEnglish
Publication NameBounded Gaps between Primes : the Epic Breakthroughs of the Early Twenty-First Century
SubjectGeneral, Number Theory
Publication Year2021
TypeTextbook
Subject AreaMathematics
AuthorKevin Broughan
FormatTrade Paperback
Dimensions
Item Height1.3 in
Item Weight36 Oz
Item Length9.6 in
Item Width6.7 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN2020-043768
Dewey Edition23
Reviews'The author has gathered almost 100 year's worth of progress on this family of problems into one volume, and this alone will be very helpful to anyone pursuing research in the field. Recommended.' M. Bona, Choice
IllustratedYes
Dewey Decimal512.73
Table Of Content1. 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.
SynopsisSearching for small gaps between consecutive primes is one way to approach the twin primes conjecture, one of the most celebrated unsolved problems in number theory. This book documents the remarkable developments of recent decades, whereby an upper bound on the known gap length between infinite numbers of consecutive primes has been reduced to a tractable finite size. The text is both introductory and complete: the detailed way in which results are proved is fully set out and plenty of background material is included. The reader journeys from selected historical theorems to the latest best result, exploring the contributions of a vast array of mathematicians, including Bombieri, Goldston, Motohashi, Pintz, Yildirim, Zhang, Maynard, Tao and Polymath8. The book is supported by a linked and freely-available package of computer programs. The material is suitable for graduate students and of interest to any mathematician curious about recent breakthroughs in the field., 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.
LC Classification NumberQA246.B743 2021
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