{"product_id":"fractal-geometry-and-number-theory-michel-l-lapidus-9781461253167","title":"Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings and Zeros of Zeta Functions","description":"A fractal drum is a bounded open subset of R. m with a fractal boundary. A difficult problem is to describe the relationship between the shape (geo- metry) of the drum and its sound (its spectrum). 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. We refer the reader to [Berrl-2, Lapl-4, LapPol-3, LapMal-2, HeLapl-2] and the ref- erences therein for further physical and mathematical motivations of this work. (Also see, in particular, Sections 7. 1, 10. 3 and 10. 4, along with Ap- pendix B. ) In Chapter 1, we introduce the basic object of our research, fractal strings (see [Lapl-3, LapPol-3, LapMal-2, HeLapl-2]). A 'standard fractal string' is a bounded open subset of the real line. Such a set is a disjoint union of open intervals, the lengths of which form a sequence which we assume to be infinite. Important information about the geometry of . c is contained in its geometric zeta function (c(8) = L lj. j=l 2 Introduction We assume throughout that this function has a suitable meromorphic ex- tension. The central notion of this book, the complex dimensions of a fractal string . c, is defined as the poles of the meromorphic extension of (c.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Michel L. Lapidus, Machiel Van Frankenhuysen\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 1461253160\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9781461253167\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Birkhauser\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 06\/13\/2012\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 268\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.89lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.60d","brand":"Michel L. Lapidus","offers":[{"title":"Paperback","offer_id":46962611060991,"sku":"9781461253167","price":54.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_5695a71f-7ba7-448b-9d57-b5ba4fdbe9cf.jpg?v=1750651984","url":"https:\/\/www.whiterainbookhouse.com\/products\/fractal-geometry-and-number-theory-michel-l-lapidus-9781461253167","provider":"WR Book House","version":"1.0","type":"link"}