2008;
558 pp;
Hardcover

MSC: Primary 11; 28; 37; 46; 58; 81;

Print ISBN: 978-0-8218-4222-5

Product Code: MBK/51

List Price: $86.00

Individual Member Price: $68.80

**Electronic ISBN: 978-1-4704-2482-4
Product Code: MBK/51.E**

List Price: $86.00

Individual Member Price: $68.80

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#### Supplemental Materials

# In Search of the Riemann Zeros: Strings, Fractal Membranes and Noncommutative Spacetimes

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*Michel L. Lapidus*

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 possible—or, 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
crystal-like, 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 & Endorsements

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