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

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Kevin Broughan (University of Waikato, New Zealand)

Bounded Gaps Between Primes

The Epic Breakthroughs of the Early Twenty-First Century

Kevin Broughan (University of Waikato, New Zealand)

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English

Cambridge University Press
25 February 2021

Mathematics & Sciences; Number theory; History of mathematics

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.

By: Kevin Broughan (University of Waikato New Zealand)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 243mm, Width: 170mm, Spine: 32mm
Weight: 1.020kg
ISBN: 9781108799201
ISBN 10: 1108799205
Pages: 590
Publication Date: 25 February 2021
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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).

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

'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 '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