
Preface  Preview Material  Table of Contents  Supplementary Material 
2008; 558 pp; hardcover ISBN10: 0821842226 ISBN13: 9780821842225 List Price: US$81 Member Price: US$64.80 Order Code: MBK/51 See also: Noncommutative Geometry, Quantum Fields and Motives  Alain Connes and Matilde Marcolli Modular Forms and String Duality  Noriko Yui, Helena Verrill and Charles F Doran  Formulated in 1859, the Riemann Hypothesis is the most celebrated and multifaceted open problem in mathematics. In essence, it states that the primes are distributed as harmoniously as possibleor, equivalently, that the Riemann zeros are located on a single vertical line, called the critical line. In this book, the author proposes a new approach to understand and possibly solve the Riemann Hypothesis. His reformulation builds upon earlier (joint) work on complex fractal dimensions and the vibrations of fractal strings, combined with string theory and noncommutative geometry. Accordingly, it relies on the new notion of a fractal membrane or quantized fractal string, along with the modular flow on the associated moduli space of fractal membranes. Conjecturally, under the action of the modular flow, the spacetime geometries become increasingly symmetric and crystallike, hence, arithmetic. Correspondingly, the zeros of the associated zeta functions eventually condense onto the critical line, towards which they are attracted, thereby explaining why the Riemann Hypothesis must be true. Written with a diverse audience in mind, this unique book is suitable for graduate students, experts and nonexperts alike, with an interest in number theory, analysis, dynamical systems, arithmetic, fractal or noncommutative geometry, and mathematical or theoretical physics. Readership Graduate students and research mathematicians interested in number theory, noncommutative geometry, and physics. Reviews "The author and the AMS have done an excellent job in the production of the book. ... Overall, this is a very interesting and very unconventional book."  Mathematicial Reviews 


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