{"product_id":"9781461421757","title":"Springer Monographs in Mathematics: Geometry and Spectra of Fractal Strings","description":"\u003ch1\u003eSpringer Monographs in Mathematics: Geometry and Spectra of Fractal Strings\u003c\/h1\u003e \u003ch2\u003eLapidus, Michel L.; van Frankenhuijsen, Machiel\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eNumber 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.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eKey Features of this Second Edition:\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings\u003c\/p\u003e\u003cp\u003eComplex 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\u003c\/p\u003e\u003cp\u003eExplicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal\u003c\/p\u003e\u003cp\u003eExamples of such explicit formulas include a Prime Orbit Theorem with error term for self-similar flows, and a geometric tube formula\u003c\/p\u003e\u003cp\u003eThe method of Diophantine approximation is used to study self-similar strings and flows \u003c\/p\u003e\u003cp\u003eAnalytical and geometric methodsare used to obtain new results about the vertical distribution of zeros of number-theoretic and other zeta functions\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThroughout, 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.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe significant studies and problems illuminated in this work may be used in a classroom setting at the graduate level. \u003ci\u003eFractal Geometry, Complex Dimensions and Zeta Functions, \u003c\/i\u003eSecond Edition will appeal to students and researchers in number theory, fractal geometry, dynamical systems, spectral geometry, and mathematical physics.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2012-09-20\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9781461421757\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-1-4614-2176-4\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 570\u003c\/p\u003e ","brand":"Springer New York","offers":[{"title":"Default Title","offer_id":44521597108364,"sku":"9781461421757","price":143.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9781461421757.jpg?v=1775706011","url":"https:\/\/lateknightbooks.com\/products\/9781461421757","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}