# 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.

ISBN-13: 978-0817640989.

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.

Usually ships within 4 to 5 days.

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).