This book presents the Riemann Hypothesis, connected problems, and a taste of the body of theory developed towards its solution. It is targeted at the educated non-expert. Almost all the material is accessible to any senior mathematics student, and much is accessible to anyone with some university mathematics.
to the Riemann Hypothesis.- Why This Book.- Analytic Preliminaries.- Algorithms for Calculating ?(s).- Empirical Evidence.- Equivalent Statements.- Extensions of the Riemann Hypothesis.- Assuming the Riemann Hypothesis and Its Extensions ....- Failed Attempts at Proof.- Formulas.- Timeline.- Original Papers.- Expert Witnesses.- The Experts Speak for Themselves.
From the reviews:
"The Reimann Hypothesis presents itself as fundamentally a collection of well-known papers related to the Reimann Hypothesis, with a long introduction to set the stage. ... This may be a useful resource for small libraries ... and for those who might like to have copies of the papers in their personal library." (Fernando Q. Gouvêa, MathDL, January, 2008)
"This book is intended as a reference work on the Riemann Hypothesis (RH). ... will undoubtedly be extremely useful for anyone making a serious study of the zeta-function, and especially those with an interest in the historical development of the subject. The choice of the material is good, and the discussion is helpful. ... anyone working in the area will benefit from a study of them. Overall this is a book which belongs on the shelves of anyone interested in the RH." (Roger Heath-Brown, Zentralblatt MATH, Vol. 1132 (10), 2008)
"Borwein (Simon Fraser Univ.) and others have compiled mostly classic papers contributing to the theory of the distribution of prime numbers. ... Summing Up: Recommended. Upper-division undergraduate through researchers/faculty." (D. V. Feldman, CHOICE, Vol. 45 (11), August, 2008)
"This delightfully written book on the Riemann Hypothesis is a welcome addition to the literature. ... its structure makes it an ideal choice as a textbook for a reading course on the Riemann zeta function and its applications, especially in classes with students of diverse mathematical backgrounds and abilities. ... I thoroughly enjoyed reading this book. ... It is a great service to have them collected in one place, and this will increase the number of mathematicians who read them." (Steven Joel Miller, Mathematical Reviews, Issue 2009 k)
"This beautiful book is an in-depth introduction to the Riemann hypothesis, arguably the most famous unsolved problem of mathematics. ... the book will also be of interest for anyone with an interest in the history of this result. ... For everyone else it is a most valuable resource of information on a fascinating conjecture and a most welcome addition to the literature." (C. Baxa, Monatshefte für Mathematik, Vol. 160 (3), June, 2010)
Preface.- Why this book.- Analytic preliminaries.- Algorithms for calculating.- Empirical evidence.- Equivalent statements.- Extensions of the riemann hypothesis.- Assuming the riemann hypothesis and its extensions.- Failed attempts at proof.- Formulas.- Timeline.- Expert witnesses.- The experts speak for themselves.- References.- References.- Index.-
This book presents the Riemann Hypothesis, connected problems, and a taste of the body of theory developed towards its solution. It is targeted at the educated non-expert. Almost all the material is accessible to any senior mathematics student, and much is accessible to anyone with some university mathematics. The appendices include a selection of original papers that encompass the most important milestones in the evolution of theory connected to the Riemann Hypothesis. The appendices also include some authoritative expository papers. These are the "expert witnesses" whose insight into this field is both invaluable and irreplaceable.