Fractal Geometry, Complex Dimensions and Zeta Functions : Geometry and Spectra of Fractal Strings
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The work Fractal Geometry, Complex Dimensions and Zeta Functions : Geometry and Spectra of Fractal Strings represents a distinct intellectual or artistic creation found in Boston University Libraries. This resource is a combination of several types including: Work, Language Material, Books.
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Fractal Geometry, Complex Dimensions and Zeta Functions : Geometry and Spectra of Fractal Strings
Resource Information
The work Fractal Geometry, Complex Dimensions and Zeta Functions : Geometry and Spectra of Fractal Strings represents a distinct intellectual or artistic creation found in Boston University Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Fractal Geometry, Complex Dimensions and Zeta Functions : Geometry and Spectra of Fractal Strings
 Title remainder
 Geometry and Spectra of Fractal Strings
 Statement of responsibility
 by Michel L. Lapidus, Machiel van Frankenhuijsen
 Subject

 Differential equations, partial
 Differential equations, partial
 Differential equations, partial
 Dynamical Systems and Ergodic Theory
 Electronic resources
 Functional Analysis
 Functional Analysis
 Functional Analysis
 Functional analysis
 Functional analysis
 Functional analysis
 Global Analysis and Analysis on Manifolds
 Global analysis
 Mathematics
 Mathematics
 Mathematics
 Measure and Integration
 Number Theory
 Number Theory
 Number Theory
 Number theory
 Number theory
 Number theory
 Partial Differential Equations
 Differentiable dynamical systems
 Differentiable dynamical systems
 Differentiable dynamical systems
 Language
 eng
 Summary

 Number theory, spectral geometry, and fractal geometry are interlinked in this indepth study of the vibrations of fractal strings; that is, onedimensional drums with fractal boundary. This second edition of Fractal Geometry, Complex Dimensions and Zeta Functions will appeal to students and researchers in number theory, fractal geometry, dynamical systems, spectral geometry, complex analysis, distribution theory, and mathematical physics. The significant studies and problems illuminated in this work may be used in a classroom setting at the graduate level. Key Features include: · The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings · Complex dimensions of a fractal string are studied in detail, and 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 selfsimilar flows, and a geometric tube formula · The method of Diophantine approximation is used to study selfsimilar strings and flows · Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of numbertheoretic and other zeta functions The unique viewpoint of this book culminates in the definition of fractality as the presence of nonreal complex dimensions. The final chapter (13) is new to the second edition and discusses several new topics, results obtained since the publication of the first edition, and suggestions for future developments in the field. Review of the First Edition: " The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actually has many applications." —NicolaeAdrian Secelean, Zentralblatt Key Features include: · The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings · Complex dimensions of a fractal string are studied in detail, and 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 selfsimilar flows, and a geometric tube formula · The method of Diophantine approximation is used to study selfsimilar strings and flows · Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of numbertheoretic and other zeta functions The unique viewpoint of this book culminates in the definition of fractality as the presence of nonreal complex dimensions. The final chapter (13) is new to the second edition and discusses several new topics, results obtained since the publication of the first edition, and suggestions for future developments in the field. Review of the First Edition: " The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actually has many applications." —NicolaeAdrian Secelean, Zentralblatt · 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 selfsimilar flows, and a geometric tube formula · The method of Diophantine approximation is used to study selfsimilar strings and flows · Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of numbertheoretic and other zeta functions The unique viewpoint of this book culminates in the definition of fractality as the presence of nonreal complex dimensions. The final chapter (13) is new to the second edition and discusses several new topics, results obtained since the publication of the first edition, and suggestions for future developments in the field. Review of the First Edition: " The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actually has many applications." —NicolaeAdrian Secelean, Zentralblatt Key Features include: · The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings · Complex dimensions of a fractal string are studied in detail, and 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 selfsimilar flows, and a geometric tube formula · The method of Diophantine approximation is used to study selfsimilar strings and flows · Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of numbertheoretic and other zeta functions The unique viewpoint of this book culminates in the definition of fractality as the presence of nonreal complex dimensions. The final chapter (13) is new to the second edition and discusses several new topics, results obtained since the publication of the first edition, and suggestions for future developments in the field. Review of the First Edition: " The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actually has many applications." —NicolaeAdrian Secelean, Zentralblatt · 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 selfsimilar flows, and a geometric tube formula · The method of Diophantine approximation is used to study selfsimilar strings and flows · Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of numbertheoretic and other zeta functions The unique viewpoint of this book culminates in the definition of fractality as the presence of nonreal complex dimensions. The final chapter (13) is new to the second edition and discusses several new topics, results obtained since the publication of the first edition, and suggestions for future developments in the field. Review of the First Edition: " The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented
 ...The book is very well written and organized and the subject is very interesting and actually has many applications." —NicolaeAdrian Secelean, Zentralblatt · 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 selfsimilar flows, and a geometric tube formula · The method of Diophantine approximation is used to study selfsimilar strings and flows · Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of numbertheoretic and other zeta functions The unique viewpoint of this book culminates in the definition of fractality as the presence of nonreal complex dimensions. The final chapter (13) is new to the second edition and discusses several new topics, results obtained since the publication of the first edition, and suggestions for future developments in the field. Review of the First Edition: " The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actually has many applications." —NicolaeAdrian Secelean, Zentralblatt Key Features include: · The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings · Complex dimensions of a fractal string are studied in detail, and 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 selfsimilar flows, and a geometric tube formula · The method of Diophantine approximation is used to study selfsimilar strings and flows · Analytical and geometric methods are used to obtain new results
 Image bit depth
 0
 LC call number
 QA241247.5
 Literary form
 non fiction
 Series statement
 Springer Monographs in Mathematics,
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