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  1. Home
  2. Books
  3. Equivalents of the Riemann Hypothesis
  • Cited by 7
  • Volume 1: Arithmetic Equivalents
  • Kevin Broughan, University of Waikato, New Zealand
Publisher:
Cambridge University Press
Online publication date:
October 2017
Print publication year:
2017
Online ISBN:
9781108178228
DOI:
https://doi.org/10.1017/9781108178228
Subjects:
Mathematics (general), Mathematics, Abstract Analysis, Number Theory
Series:
Encyclopedia of Mathematics and its Applications (164)
Information

Book description

The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions repeated, proofs split into logical sections, and graphical descriptions of the relations between different results. It also includes extensive tables, supplementary computational tools, and open problems suitable for research. Accompanying software is free to download. These books will interest mathematicians who wish to update their knowledge, graduate and senior undergraduate students seeking accessible research problems in number theory, and others who want to explore and extend results computationally. Each volume can be read independently. Volume 1 presents classical and modern arithmetic equivalents to RH, with some analytic methods. Volume 2 covers equivalences with a strong analytic orientation, supported by an extensive set of appendices containing fully developed proofs.

Reviews

'This two volume catalogue of many of the various equivalents of the Riemann Hypothesis by Kevin Broughan is a valuable addition to the literature … all in all these two volumes are a must have for anyone interested in the Riemann Hypothesis.'

Steven Decke Source: MAA Reviews

'Throughout the book careful proofs are given for all the results discussed, introducing an impressive range of mathematical tools. Indeed, the main achievement of the work is the way in which it demonstrates how all these diverse subject areas can be brought to bear on the Riemann hypothesis. The exposition is accessible to strong undergraduates, but even specialists will find material here to interest them.'

D. R. Heath-Brown Source: Mathematical Reviews

‘All in all these books serve as a good introduction to a wide range of mathematics related to the Riemann Hypothesis and make for a valuable contribution to the literature. They are truly encyclopedic and I am sure will entice many a reader to consult some literature quoted and who knows, eventually make an own contribution to the area.’

Pieter Moree Source: Nieuw Archief voor Wiskunde

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Contents

Contents
References
References
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