{"product_id":"fractal-geometry-and-number-theory-complex-dimensions-of-fractal","title":"Fractal Geometry and Number Theory: Complex Dimensions of Fractal","description":"\u003cp\u003eIn this review of Fractal Geometry and Number Theory, the authors tackle a specialized intersection of analysis, geometry and number theory aimed at researchers and advanced graduate students; the single biggest reason to buy is its sustained development of the theory of \u003cstrong\u003ecomplex dimensions\u003c\/strong\u003e for fractal strings and their connection to spectral properties. The book limits its scope to one-dimensional fractal strings and higher dimensional analogues called fractal sprays, making it a focused resource rather than a broad textbook, and the review highlights where it is most useful and what readers should expect.\u003c\/p\u003e\n\u003ch2\u003eKey Features\u003c\/h2\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eTheory of complex dimensions:\u003c\/strong\u003e The book systematically develops complex dimensions for fractal strings, giving a coherent framework for relating geometry to spectral data.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eFocus on fractal strings:\u003c\/strong\u003e By restricting to one-dimensional fractal strings and fractal sprays, the text provides concentrated treatment that benefits readers seeking depth over breadth.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eConnections to zeta zeros:\u003c\/strong\u003e The work examines links between complex dimensions and zeros of zeta functions, useful for readers interested in analytic number theory aspects.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eReferenced background:\u003c\/strong\u003e The authors situate results with extensive references to prior literature, which aids further reading and context for motivated researchers.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eStructured chapters and appendices:\u003c\/strong\u003e Early chapters introduce core objects and later sections and appendices offer targeted technical material, making navigation practical for study and reference.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eWho It's For\u003c\/h2\u003e\n\u003cp\u003eThis book is best for mathematicians, advanced graduate students and researchers who already have a solid background in analysis, spectral theory or analytic number theory and who want a rigorous account of how geometry and spectrum interact in the fractal string setting. It is particularly suitable for those researching fractal geometry, zeta functions or spectral asymptotics.\u003c\/p\u003e\n\u003cp\u003eReaders new to these fields or seeking broad introductions to geometry or number theory should look elsewhere for a gentler entry-level text; this is not a general textbook but a specialist monograph that assumes familiarity with advanced mathematical tools.\u003c\/p\u003e\n\u003ch2\u003ePros \u0026amp; Cons\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003ePros\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eDeep, focused development of \u003cstrong\u003ecomplex dimensions\u003c\/strong\u003e that clarifies links between geometry and spectrum.\u003c\/li\u003e\n\u003cli\u003eCareful treatment of fractal strings and fractal sprays, valuable for specialists studying one-dimensional analogues.\u003c\/li\u003e\n\u003cli\u003eExtensive references and cross-references to foundational work, aiding follow-up research.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eSpecialist level and narrow scope make it less accessible to readers without strong background in analysis and number theory.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eSpecifications\u003c\/h2\u003e\n\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003eTitle\u003c\/td\u003e\n\u003ctd\u003eFractal Geometry and Number Theory\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAuthors\u003c\/td\u003e\n\u003ctd\u003eMichel L. L. Lapidus, Machiel van Frankenhuysen\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePrimary subjects\u003c\/td\u003e\n\u003ctd\u003eFractal strings, fractal sprays, zeta functions\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eFocus\u003c\/td\u003e\n\u003ctd\u003eComplex dimensions and relations between geometry and spectrum\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eScope\u003c\/td\u003e\n\u003ctd\u003eOne-dimensional fractal strings and higher dimensional analogues\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eIncludes\u003c\/td\u003e\n\u003ctd\u003eChapters with technical sections and appendix material\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n\u003ch2\u003eOur Verdict\u003c\/h2\u003e\n\u003cp\u003eFor researchers and advanced students who want a rigorous, concentrated account of complex dimensions and their relation to zeta zeros and spectral questions, this book is a valuable and well-referenced resource; its specialist focus and technical depth make it good value for those with the required background but less suitable as an introductory text.\u003c\/p\u003e\n\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003eIs this book introductory?\u003c\/strong\u003e\u003cbr\u003eNo, it is a specialist monograph that assumes familiarity with advanced analysis and number theory rather than a first course introduction.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eDoes it cover higher dimensions?\u003c\/strong\u003e\u003cbr\u003eWhile the core development is for one-dimensional fractal strings, the book treats higher dimensional analogues called fractal sprays and discusses relevant extensions.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eAre there pointers to further reading?\u003c\/strong\u003e\u003cbr\u003eYes, the authors provide numerous references and specific sections and appendices that guide readers to foundational and follow-up literature.\u003c\/p\u003e","brand":"Michel L. L. Lapidus, Machiel van Frankenhuysen","offers":[{"title":"Default Title","offer_id":48662433464539,"sku":"1461253160","price":54.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0724\/1043\/1707\/files\/51mwYyheAOL._SL1259.jpg?v=1778702427","url":"https:\/\/gearmusthave.com\/products\/fractal-geometry-and-number-theory-complex-dimensions-of-fractal","provider":"GearMustHave","version":"1.0","type":"link"}