Fractal Geometry and Number Theory ebook
by Machiel van Frankenhuysen,Michel L. Lapidus
In this book, we restrict ourselves to the one-dimensional case of fractal . A Zeta Functions in Number Theory.
In this book, we restrict ourselves to the one-dimensional case of fractal strings, and their higher dimensional analogues, fractal sprays. We develop a theory of complex di mensions of a fractal string, and we study how these complex dimensions relate the geometry with the spectrum of the fractal string. 221. B Zeta Functions of Laplacians and Spectral Asymptotics. Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings.
Includes a geometric reformulation of the Riemann hypothesis and a new final chapter on recent topics and results.
Van Frankenhuijsen, Machiel, The Riemann Hypothesis for Function Fields: Frobenius Flow and Shift Operators, London Mathematical Society Student Texts (Book 80), Cambridge University Press (January 9, 2014), 162 pp.
eBook n/a. ISBN 978-1-4612-5314-3.
This is a two-part volume. Part 1 covers analysis, number theory, and dynamical systems; Part 2, multifractals, probability and statistical mechanics, and applications.
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Fractal Geometry and Number Theory. Number theory and fractal geometry are combined in this study of the vibrations of fractal strings. The book centres around a notion of complex dimension, originally developed for the proof of th. More).