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

Broughan, Kevin

ISBN 10: 1108836747 / ISBN 13: 9781108836746

Published by Cambridge University Press, 2021

About this Item

Seller Inventory # I-9781108836746

Bibliographic Details

• Title: Bounded Gaps Between Primes: The Epic Breakthroughs of the Early Twenty-First Century
• Publisher: Cambridge University Press
• Publication Date: 2021
• Language: English
• ISBN 10: 1108836747
• ISBN 13: 9781108836746
• Binding: Hardcover
• Condition: New

About this title

Synopsis

Searching 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.

About the Author

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).