Fractal Geometry, Complex Dimensions and Zeta Functions

Michel L. Lapidus, Machiel Van Frankenhuijsen - Collection Springer Monographs in Mathematics

460 pages, parution le 31/08/2006

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Résumé

Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. In this book The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings. The book also offers explicit formulas extended to apply to the geometric, spectral, and dynamic zeta functions associated with a fractal. In addition, numerous theorems, examples, remarks and illustrations enrich the text.

Sommaire

Complex dimensions of ordinary fractal strings
Complex dimensions of self-similar fractal strings
Complex dimensions of nonlattice self-similar strings : quasiperiodic patterns and diophantine approximation
Generalized fractal strings viewed as measures
Explicit formulas for generalized fractal strings
The geometry and the spectrum of fractal strings
Periodic orbits of self-similar flows
Tubular neighborhoods and Minkowski measurability
The Riemann hypothesis and inverse spectral problems
Generalized cantor strings and their oscillations
The critical zeros of zeta functions
Concluding comments, open problems, and perspectives
AZeta functions in number theory
BZeta functions of Laplacians and spectral asymptotics
CAn application of Nevanlinna theory

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	PAPIER
Éditeur(s)	Springer
Auteur(s)	Michel L. Lapidus, Machiel Van Frankenhuijsen
Collection	Springer Monographs in Mathematics
Parution	31/08/2006
Nb. de pages	460
Format	16 x 24
Couverture	Relié
Poids	816g
Intérieur	Noir et Blanc
EAN13	9780387332857
ISBN13	978-0-387-33285-7