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

Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings (Springer Monographs in Mathematics)

Science & Math

Lapidus, Michel L.

van Frankenhuijsen, Machiel

Mathematics

Springer

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.
Throughout Geometry, Complex Dimensions and Zeta Functions, Second Edition, new results are examined and a new definition of fractality as the presence of nonreal complex dimensions with positive real parts is presented. The new final chapter discusses several new topics and results obtained since the publication of the first edition.

Reference

In its Second Edition, this in-depth study of the vibrations of fractal strings interlinks number theory, spectral geometry and fractal geometry. Includes a geometric reformulation of the Riemann hypothesis and a new final chapter on recent topics and results.

See the best price to sell, buy, or rent books by van Frankenhuijsen, Machiel. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by van Frankenhuijsen, Machiel

See the best price to sell, buy, or rent books by van Frankenhuijsen, Machiel. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings (Springer Monographs in Mathematics)

Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings (Springer Monographs in Mathematics)

Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings (Springer Monographs in Mathematics)