LEADER 04640nam 2200661 a 450 001 9910438156403321 005 20200520144314.0 010 $a1-283-90955-3 010 $a1-4614-2176-4 024 7 $a10.1007/978-1-4614-2176-4 035 $a(CKB)3400000000086013 035 $a(EBL)1081817 035 $a(OCoLC)811139645 035 $a(SSID)ssj0000767029 035 $a(PQKBManifestationID)11414646 035 $a(PQKBTitleCode)TC0000767029 035 $a(PQKBWorkID)10732101 035 $a(PQKB)10450451 035 $a(DE-He213)978-1-4614-2176-4 035 $a(MiAaPQ)EBC1081817 035 $a(PPN)168295873 035 $a(EXLCZ)993400000000086013 100 $a20120830d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFractal geometry, complex dimensions and zeta functions $egeometry and spectra of fractal strings /$fMichel L. Lapidus, Machiel van Frankenhuijsen 205 $a2nd ed. 210 $aNew York $cSpringer$d2013 215 $a1 online resource (582 p.) 225 0$aSpringer monographs in mathematics,$x1439-7382 300 $a"With 73 illustrations." 311 $a1-4899-8838-6 311 $a1-4614-2175-6 320 $aIncludes bibliographical references and indexes. 327 $aPreface -- Overview -- Introduction -- 1. Complex Dimensions of Ordinary Fractal Strings -- 2. Complex Dimensions of Self-Similar Fractal Strings -- 3. Complex Dimensions of Nonlattice Self-Similar Strings -- 4. Generalized Fractal Strings Viewed as Measures -- 5. Explicit Formulas for Generalized Fractal Strings -- 6. The Geometry and the Spectrum of Fractal Strings -- 7. Periodic Orbits of Self-Similar Flows -- 8. Fractal Tube Formulas -- 9. Riemann Hypothesis and Inverse Spectral Problems -- 10. Generalized Cantor Strings and their Oscillations -- 11. Critical Zero of Zeta Functions -- 12 Fractality and Complex Dimensions -- 13. Recent Results and Perspectives -- Appendix A. Zeta Functions in Number Theory -- Appendix B. Zeta Functions of Laplacians and Spectral Asymptotics -- Appendix C. An Application of Nevanlinna Theory -- Bibliography -- Author Index -- Subject Index -- Index of Symbols -- Conventions -- Acknowledgements. 330 $aNumber theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings; that is, one-dimensional drums with fractal boundary. This second edition of Fractal Geometry, Complex Dimensions and Zeta Functions will appeal to students and researchers in number theory, fractal geometry, dynamical systems, spectral geometry, complex analysis, distribution theory, and mathematical physics. The significant studies and problems illuminated in this work may be used in a classroom setting at the graduate level. Key Features include: The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings · Complex dimensions of a fractal string are studied in detail, and used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra · Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal ·  Examples of such explicit formulas include a Prime Orbit Theorem with error term for self-similar flows, and a geometric tube formula ·  The method of Diophantine approximation is used to study self-similar strings and flows · Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of number-theoretic and other zeta functions The unique viewpoint of this book culminates in the definition of fractality as the presence of nonreal complex dimensions. The final chapter (13) is new to the second edition and discusses several new topics, results obtained since the publication of the first edition, and suggestions for future developments in the field. 410 0$aSpringer Monographs in Mathematics,$x1439-7382 606 $aFractals 606 $aFunctions, Zeta 606 $aGeometry, Riemannian 606 $aNumber theory 615 0$aFractals. 615 0$aFunctions, Zeta. 615 0$aGeometry, Riemannian. 615 0$aNumber theory. 676 $a514.742 700 $aLapidus$b Michel L$047890 701 $aFrankenhuijsen$b Machiel van$0724893 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438156403321 996 $aFractal geometry, complex dimensions and zeta functions$91416625 997 $aUNINA LEADER 01069nam0 22002531i 450 001 UON00414985 005 20231205104756.890 100 $a20121212d1969 |0itac50 ba 101 $aeng 102 $aUS 105 $a|||| 1|||| 200 1 $aˆA ‰manual of comparative romance linguistics$ephonology and morphology$fby Henry Mendeloff 210 $aWashington$cThe Catholic University of America Press$d1969 215 $axiv, 123 p.: ill.$d24 cm. 606 $aLinguistica$xEuropa$xOrigini e sviluppi$3UONC060548$2FI 676 $a417.7$cLinguistica storica$v21 700 1$aMENDELOFF$bHenry$3UONV211963$0200639 712 $aCatholic University of America Press$3UONV252527$4650 801 $aIT$bSOL$c20251024$gRICA 899 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$2UONSI 912 $aUON00414985 950 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$dSI Fil.R A 224 $eSI LO 2434 5 224 $sBuono 996 $aManual of comparative Romance linguistics$9138914 997 $aUNIOR