{"title":"Michel L Lapidus","description":null,"products":[{"product_id":"fractal-geometry-complex-dimensions-and-zeta-functions-book-michel-l-lapidus-9781461421757","title":"Fractal Geometry, Complex Dimensions and Zeta Functions","description":"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.    Key Features of this Second Edition:    The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings  Complex 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  Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal  Examples of such explicit formulas include a Prime Orbit Theorem with error term for self-similar flows, and a geometric tube formula  The method of Diophantine approximation is used to study self-similar strings and flows   Analytical and geometric methodsare used to obtain new results about the vertical distribution of zeros of number-theoretic and other zeta functions    Throughout, 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.    The significant studies and problems illuminated in this work may be used in a classroom setting at the graduate level. Fractal Geometry, Complex Dimensions and Zeta Functions, Second Edition will appeal to students and researchers in number theory, fractal geometry, dynamical systems, spectral geometry, and mathematical physics.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":49734090326289,"sku":"NGR9781461421757","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52593648173329,"sku":"NLS9781461421757","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1461421756.jpg?v=1751306255"},{"product_id":"in-search-of-the-riemann-zeros-book-michel-l-lapidus-9780821842225","title":"In Search of the Riemann Zeros","description":"Formulated in 1859, the Riemann Hypothesis is the most celebrated and multifaceted open problem in mathematics. In essence, it states that the primes are distributed as harmoniously as possible--or, equivalently, that the Riemann zeros are located on a single vertical line, called the critical line.","brand":"WoB","offers":[{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":50097154228497,"sku":"CIN0821842226VG","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ GOOD \/ SBYB","offer_id":52607866798353,"sku":"CIN0821842226G","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0821842226.jpg?v=1751107017"},{"product_id":"invitation-to-fractal-geometry-book-michel-l-lapidus-9781470478957","title":"An Invitation to Fractal Geometry","description":"This book offers a comprehensive exploration of fractal dimensions, self-similarity, and fractal curves. Targeting undergraduate and graduate students, postdocs, mathematicians, and scientists across disciplines, this text requires minimal prerequisites beyond a solid foundation in undergraduate mathematics. While fractal geometry may seem esoteric, this book demystifies it by providing a thorough introduction to its mathematical underpinnings and applications. Complete proofs are provided for most of the key results, and exercises of different levels of difficulty are proposed throughout the book.  Key topics covered include the Hausdorff metric, Hausdorff measure, and fractal dimensions such as Hausdorff and Minkowski dimensions. The text meticulously constructs and analyzes Hausdorff measure, offering readers a deep understanding of its properties. Through emblematic examples like the Cantor set, the Sierpinski gasket, the Koch snowflake curve, and the Weierstrass curve, readers are introduced to self-similar sets and their construction via the iteration of contraction mappings.  The book also sets the stage for the advanced theory of complex dimensions and fractal drums by gently introducing it via a variety of classical examples, including well-known fractal curves. By intertwining historical context with rigorous mathematical exposition, this book serves as both a stand-alone resource and a gateway to deeper explorations in fractal geometry.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51627308089617,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ GARDNERS","offer_id":51627308351761,"sku":"NGR9781470478957","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1470478951.jpg?v=1757415239"},{"product_id":"fractal-geometry-and-number-theory-book-michel-l-lapidus-9780817640989","title":"Fractal Geometry and Number Theory","description":"This book should appeal to geometers, fractalists, mathematical physicists and number theorists, as well as to graduate students in these fields and others interested in gaining insight into these rich areas either for its own sake or with a view to applications.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52133454217489,"sku":"NLS9780817640989","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780817640989.jpg?v=1757530538"},{"product_id":"fractal-geometry-complex-dimensions-and-zeta-functions-book-michel-l-lapidus-9781489988386","title":"Fractal Geometry, Complex Dimensions and Zeta Functions","description":"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.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52146124325137,"sku":"NLS9781489988386","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781489988386.jpg?v=1757596581"},{"product_id":"fractal-zeta-functions-and-fractal-drums-book-michel-l-lapidus-9783319447049","title":"Fractal Zeta Functions and Fractal Drums","description":"Overview.- Preface.- List of Figures.- Key Words.- Selected Key Results.- Glossary.- 1. Introduction.- 2 Distance and Tube Zeta Functions.- 3. Applications of Distance and Tube Zeta Functions.- 4. Relative Fractal Drums and Their Complex Dimensions.- 5.Fractal Tube Formulas and Complex Dimensions.- 6. Classification of Fractal Sets and Concluding Comments.- Appendix A. Tame Dirchlet-Type Integrals.- Appendix B. Local Distance Zeta Functions.- Appendix C. Distance Zeta Functions and Principal Complex Dimensions of RFDs.- Acknowledgements.- Bibliography.- Author Index.- Subject Index.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52339276677393,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52339280707857,"sku":"NLS9783319447049","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783319447049.jpg?v=1758169576"},{"product_id":"fractal-zeta-functions-and-fractal-drums-book-michel-l-lapidus-9783319831152","title":"Fractal Zeta Functions and Fractal Drums","description":"Overview.- Preface.- List of Figures.- Key Words.- Selected Key Results.- Glossary.- 1. Introduction.- 2 Distance and Tube Zeta Functions.- 3. Applications of Distance and Tube Zeta Functions.- 4. Relative Fractal Drums and Their Complex Dimensions.- 5.Fractal Tube Formulas and Complex Dimensions.- 6. Classification of Fractal Sets and Concluding Comments.- Appendix A. Tame Dirchlet-Type Integrals.- Appendix B. Local Distance Zeta Functions.- Appendix C. Distance Zeta Functions and Principal Complex Dimensions of RFDs.- Acknowledgements.- Bibliography.- Author Index.- Subject Index.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52532810449169,"sku":"NLS9783319831152","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783319831152.jpg?v=1760662369"},{"product_id":"fractal-geometry-and-number-theory-book-michel-l-lapidus-9781461253167","title":"Fractal Geometry and Number Theory","description":"This book should appeal to geometers, fractalists, mathematical physicists and number theorists, as well as to graduate students in these fields and others interested in gaining insight into these rich areas either for its own sake or with a view to applications.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52650524705041,"sku":"NLS9781461253167","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52750016741649,"sku":"NIN9781461253167","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461253167.jpg?v=1762128207"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-michel-l-lapidus.oembed","provider":"World of Books ","version":"1.0","type":"link"}