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Library,Documentation and Information Science Division

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-P.C.Mahalanobis


Fractal Geometry, Complex Dimensions and Zeta Functions (Record no. 425116)

000 -LEADER
fixed length control field 05772nam a22005895i 4500
020 ## - INTERNATIONAL STANDARD BOOKNUMBER
International Standard Book Number 9780387352084
-- 978-0-387-35208-4
024 7# -
-- 10.1007/978-0-387-35208-4
-- doi
040 ## -
-- ISI Library, Kolkata
050 #4 -
-- QA611-614.97
072 #7 -
-- PBP
-- bicssc
072 #7 -
-- MAT038000
-- bisacsh
072 #7 -
-- PBP
-- thema
082 04 - DEWEYDECIMAL CLASSIFICATION NUMBER
Classification number 514
Edition number 23
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Lapidus, Michel L.
Relator code aut
-- http://id.loc.gov/vocabulary/relators/aut
245 10 - TITLE STATEMENT
Title Fractal Geometry, Complex Dimensions and Zeta Functions
Medium [electronic resource] :
Remainder of title Geometry and Spectra of Fractal Strings /
Statement of responsibility, etc by Michel L. Lapidus, Machiel van Frankenhuijsen.
942 ## - ADDED ENTRY ELEMENTS(KOHA)
Koha item type E-BOOKS
100 1# - MAIN ENTRY--PERSONAL NAME
-- author.
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE STATEMENTS
Place of production, publication, distribution, manufacture New York, NY :
Name of producer, publisher, distributor, manufacturer Springer New York,
Date of production, publication, distribution, manufacture 2006.
300 ## -
-- XXIV, 460 p. 54 illus.
-- online resource.
336 ## - CONTENT TYPE
Content Type Term text
Content Type Code txt
Source rdacontent
337 ## - MEDIA TYPE
Media Type Term computer
Media Type Code c
Source rdamedia
338 ## - CARRIER TYPE
Carrier Type Term online resource
Carrier Type Code cr
Source rdacarrier
347 ## -
-- text file
-- PDF
-- rda
490 1# -
-- Springer Monographs in Mathematics,
-- 1439-7382
505 0# -
-- 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.
520 ## -
-- 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. Key Features The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings Complex dimensions of a fractal string, defined as the poles of an associated zeta function, are studied in detail, then used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal Examples of such explicit formulas include a Prime Orbit Theorem with error term for self-similar flows, and a geometric tube formula The method of Diophantine approximation is used to study self-similar strings and flows Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of number-theoretic and other zeta functions Throughout new results are examined. The final chapter gives a new definition of fractality as the presence of nonreal complex dimensions with positive real parts, and discusses several open problems and extensions. The significant studies and problems illuminated in this work may be used in a classroom setting at the graduate level. Fractal Geometry, Complex Dimensions and Zeta Functions will appeal to students and researchers in number theory, fractal geometry, dynamical systems, spectral geometry, and mathematical physics. From Reviews of Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings and Zeros of Zeta Functions, by Michel Lapidus and Machiel van Frankenhuysen, Birkhäuser Boston Inc., 2000. "This highly original self-contained book will appeal to geometers, fractalists, mathematical physicists and number theorists, as well as to graduate students in these fields and others interested in gaining insight into these rich areas either for its own sake or with a view to applications. They will find it a stimulating guide, well written in a clear and pleasant style." –Mathematical Reviews "It is the reviewer’s opinion that the authors have succeeded in showing that the complex dimensions provide a very natural and unifying mathematical framework for investigating the oscillations in the geometry and the spectrum of a fractal string. The book is well written. The exposition is self-contained, intelligent and well paced." –Bulletin of the London Mathematical Society.
650 #0 -
-- Topology.
650 #0 -
-- Number theory.
650 #0 -
-- Mathematics.
650 #0 -
-- Differential equations, partial.
650 #0 -
-- Differentiable dynamical systems.
650 #0 -
-- Global analysis.
650 14 -
-- Topology.
-- http://scigraph.springernature.com/things/product-market-codes/M28000
650 24 -
-- Number Theory.
-- http://scigraph.springernature.com/things/product-market-codes/M25001
650 24 -
-- Measure and Integration.
-- http://scigraph.springernature.com/things/product-market-codes/M12120
650 24 -
-- Partial Differential Equations.
-- http://scigraph.springernature.com/things/product-market-codes/M12155
650 24 -
-- Dynamical Systems and Ergodic Theory.
-- http://scigraph.springernature.com/things/product-market-codes/M1204X
650 24 -
-- Global Analysis and Analysis on Manifolds.
-- http://scigraph.springernature.com/things/product-market-codes/M12082
700 1# -
-- Frankenhuijsen, Machiel van.
-- author.
-- aut
-- http://id.loc.gov/vocabulary/relators/aut
710 2# -
-- SpringerLink (Online service)
773 0# -
-- Springer eBooks
776 08 -
-- Printed edition:
-- 9780387513102
776 08 -
-- Printed edition:
-- 9780387332857
830 #0 -
-- Springer Monographs in Mathematics,
-- 1439-7382
856 40 -
-- https://doi.org/10.1007/978-0-387-35208-4
912 ## -
-- ZDB-2-SMA
950 ## -
-- Mathematics and Statistics (Springer-11649)

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