Fractal geometry and number theory : complex dimensions of fractal strings and zeros of zeta functions, with 26 illustrations / Michel L. Lapidus, Machiel van Frankenhuysen.

Format:

Book

Author/Creator:

Lapidus, Michel L. (Michel Laurent), 1956-

Contributor:

Van Frankenhuysen, Machiel, 1967-

Bernard W. Freeman Book Fund.

Language:

English

Subjects (All):

Fractals.

Number theory.

Functions, Zeta.

Physical Description:

x, 268 pages : illustrations ; 25 cm

Place of Publication:

Boston : Birkhäuser, [2000]

Summary:

Can one hear the shape of a drum? The relationship between the shape (geometry) of a drum and its sound (its spectrum is an interesting and difficult problem to describe. In this monograph, an extensive study is made of this problem for one-dimensional drums with fractal strings. The work centers around the author's original research on a newly developed theory of "complex dimensions of fractal strings." All of the material is self-contained and provide a unique geometric characterization of the Riemann hypothesis.

Notes:

Includes bibliographical references and indexes.

Local Notes:

Acquired for the Penn Libraries with assistance from the Bernard W. Freeman Book Fund.

ISBN:

0817640983

OCLC:

42641760