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Umfang: 1 online resource (1129 p.)

ISBN: 9783110198133 , 9783110637205

Serie: De Gruyter Proceedings in Mathematics

Inhalt: Dieses zweibändige Werk versammelt Vorlesungen, gehalten in memoriam Professor Bernard Dwork (1923-1998), anlässlich eines dreimonatigen Vorlesungszyklus in Norditalien von Mai bis Juli 2001.

Inhalt: This two-volume book collects the lectures given during the three months cycle of lectures held in Northern Italy between May and July of 2001 to commemorate Professor Bernard Dwork (1923 - 1998). It presents a wide-ranging overview of some of the most active areas of contemporary research in arithmetic algebraic geometry, with special emphasis on the geometric applications of the p-adic analytic techniques originating in Dwork's work, their connection to various recent cohomology theories and to modular forms. The two volumes contain both important new research and illuminating survey articles written by leading experts in the field. The book will provide an indispensable resource for all those wishing to approach the frontiers of research in arithmetic algebraic geometry.

Anmerkung: Geometric Aspects of Dwork Theory. Volume I -- , Frontmatter -- , Table of Contents of Volume I -- , The Mathematical Publications of Bernard -- , Dwork -- , Exponential sums and generalized hypergeometric -- , functions. I: Cohomology spaces and Frobenius action -- , Exponential sums and free hyperplane -- , arrangements -- , Sur la conjecture des p-courbures de -- , Grothendieck-Katz et un problème de Dwork -- , Hilbert modular varieties of low dimension -- , On Dwork cohomology for singular -- , hypersurfaces -- , On Dwork cohomology and algebraic D-modules -- , An introduction to the theory of p-adic -- , representations -- , Smooth p-adic analytic spaces are locally -- , contractible. II -- , Germs of analytic varieties in algebraic varieties: -- , canonical metrics and arithmetic algebraization theorems -- , Thirty years later -- , Approximation of eigenforms of infinite slope by -- , eigenforms of finite slope -- , Crystalline cohomology of singular -- , varieties -- , Stacks of twisted modules and integral -- , transforms -- , On some rational generating series occuring in -- , arithmetic geometry -- , Compactifications arithmétiques des variétés de -- , Hilbert et formes modulaires de Hilbert pour Γ1(c, n) -- , Geometric Aspects of Dwork Theory. Volume -- , II -- , Frontmatter -- , Table of Contents of Volume II -- , Variétés et formes modulaires de Hilbert -- , arithmétiques pour Γ1(c, n) -- , Introduction to p-adic q-difference equations (weak -- , Frobenius structure and transfer theorems) -- , An introduction to the Riemann-Hilbert -- , correspondence for unit F-crystals -- , Introduction to L-functions of -- , F-isocrystals -- , Notes on some t-structures -- , Non-vanishing modulo p of Hecke L-values -- , On semistable reduction and the calculation of -- , nearby cycles -- , Inequalities related to Lefschetz pencils and -- , integrals of Chern classes -- , Full faithfulness for overconvergent -- , F-isocrystals -- , Frobenius action, F-isocrystals and slope -- , filtration -- , Conjecture on Abbes-Saito filtration and -- , Christol-Mebkhout filtration -- , Transformation de Fourier des D-modules -- , arithmétiques I -- , Boyarsky principle for D-modules and Loeser's -- , conjecture -- , Cohomological descent in rigid cohomology -- , Monodromie locale et fonctions Zêta des log -- , schémas -- , Trace et dualité relative pour les D-modules -- , arithmétiques -- , Geometric moment zeta functions , Mode of access: Internet via World Wide Web. , In English.

In: DGBA Mathematics - 2000 - 2014, De Gruyter, 9783110637205

In: E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2008, De Gruyter, 9783110212129

In: E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2008, De Gruyter, 9783110212136

In: E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2008, De Gruyter, 9783110209082

Weitere Ausg.: ISBN 9783110174786

Sprache: Englisch

Schlagwort(e): Aufsatzsammlung ; Bibliografie

DOI: 10.1515/9783110198133

URL: https://doi.org/10.1515/9783110198133

URL: https://www.degruyter.com/isbn/9783110198133

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Umfang: 1 Online-Ressource (xxviii, 293 Seiten, [68] Seiten mit Tafeln) : , Illustrationen, Karten.

ISBN: 978-90-04-21086-8 , 90-04-21086-5

Serie: Religions in the Graeco-Roman world Volume 171

Anmerkung: Includes bibliographical references (pages xi-xiv) and index. - La gens isiaque de retour au pays - Michel Malaise -- - Understanding Egypt in Egypt and beyond - Miguel John Versluys -- - Culte d'Isis ou religion isiaque? - Françoise Dunand -- - How do you want your goddess? - From the Galjub Hoard to a general vision on religious choice in Hellenistic and Roman Egypt - Frederick G. Naerebout -- - Alexandria in Aegypto - the use and meaning of Egyptian elements in Hellenistic and Roman Alexandria - Kyriakos Savvopoulos -- - Referencing Isis in tombs in Graeco-Roman Egypt - tradition and innovation - Marjorie S. Venit -- - Les formes d'Isis à Karnak à travers la prosopographie sacerdotale de l'époque Ptolémaïque - Laurent Coulon -- - Isis in Roman Dakleh - goddess of the village, the province, and the country - Olaf E. Kaper -- - Mythologie grecque ou mystère d'Isis-Déméter? - Angelo Geissen -- - Les isiaques et la petite plastique dans l'Égypte hellénistique et romaine - Pascale Ballet et Geneviève Galliano -- - Anubis mit dem Schlüssel in der kaiserzeitlichen Grabkunst Ägyptens - Youri Volokhine -- - Couronner Souchos pour fêter le retour de la crue - Pierre P. Koemoth , In English, French, and German

Weitere Ausg.: Erscheint auch als Druck-Ausgabe ISBN 978-90-04-18882-2

Sprache: Englisch

Fachgebiete: Geschichte

Schlagwort(e): Religion ; Bibliografie ; Konferenzschrift ; Festschrift

DOI: 10.1163/ej.9789004188822.i-364

URL: Volltext

Mehr zum Autor: Bricault, Laurent, 1963-

Mehr zum Autor: Versluys, Miguel John, 1971-

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Umfang: Online-Ressource (XXVI, 567 p. 73 illus, digital)

Ausgabe: 2nd ed. 2013

ISBN: 9781461421764 , 1283909553 , 9781283909556

Serie: Springer Monographs in Mathematics

Inhalt: Preface -- 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.

Inhalt: 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. 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. Review of the First Edition: " The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actually has many applications." —Nicolae-Adrian Secelean, Zentralblatt 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. Review of the First Edition: " The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actually has many applications." —Nicolae-Adrian Secelean, Zentralblatt · 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. Review of the First Edition: " The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actually has many applications." —Nicolae-Adrian Secelean, Zentralblatt 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. Review of the First Edition: " The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actually has many applications." —Nicolae-Adrian Secelean, Zentralblatt · 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. Review of the First Edition: " The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actually has many applications." —Nicolae-Adrian Secelean, Zentralblatt · 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. Review of the First Edition: " The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actually has many applications." —Nicolae-Adrian Secelean, Zentralblatt 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 dynami...

Anmerkung: Description based upon print version of record , Fractal Geometry, Complex Dimensions and Zeta Functions; Overview; Preface; Contents; List of Figures; List of Tables; Introduction; 1 Complex Dimensions of Ordinary Fractal Strings; 1.1 The Geometry of a Fractal String; 1.1.1 The Multiplicity of the Lengths; 1.1.2 Example: The Cantor String; 1.2 The Geometric Zeta Function of a Fractal String; 1.2.1 The Screen and the Window; 1.2.2 The Cantor String (continued); 1.3 The Frequencies of a Fractal String and the Spectral Zeta Function; 1.4 Higher-Dimensional Analogue: Fractal Sprays; 1.5 Notes , 2 Complex Dimensions of Self-Similar Fractal Strings2.1 Construction of a Self-Similar Fractal String; 2.1.1 Relation with Self-Similar Sets; 2.2 The Geometric Zeta Function of a Self-Similar String; 2.2.1 Self-Similar Strings with a Single Gap; 2.3 Examples of Complex Dimensions of Self-Similar Strings; 2.3.1 The Cantor String; 2.3.2 The Fibonacci String; 2.3.3 The Modified Cantor and Fibonacci Strings; 2.3.4 A String with Multiple Poles; 2.3.5 Two Nonlattice Examples: the Two-Three String and the Golden String; The Golden String; 2.4 The Lattice and Nonlattice Case , 2.5 The Structure of the Complex Dimensions2.6 The Asymptotic Density of the Poles in the Nonlattice Case; 2.7 Notes; 3 Complex Dimensions of Nonlattice Self-Similar Strings: Quasiperiodic Patterns and Diophantine Approximation; 3.1 Dirichlet Polynomial Equations; 3.1.1 The Generic Nonlattice Case; 3.2 Examples of Dirichlet Polynomial Equations; 3.2.1 Generic and Nongeneric Nonlattice Equations; 3.2.2 The Complex Roots of the Golden Plus Equation; 3.3 The Structure of the Complex Roots; 3.4 Approximating a Nonlattice Equation by Lattice Equations; 3.4.1 Diophantine Approximation , 3.4.2 The Quasiperiodic Pattern of the Complex Dimensions3.4.3 Application to Nonlattice Strings; 3.5 Complex Roots of a Nonlattice Dirichlet Polynomial; 3.5.1 Continued Fractions; 3.5.2 Two Generators; 3.5.3 More than Two Generators; 3.6 Dimension-Free Regions; 3.7 The Dimensions of Fractality of a Nonlattice String; 3.7.1 The Density of the Real Parts; 3.8 A Note on the Computations; 3.9 Notes; 4 Generalized Fractal Strings Viewed as Measures; 4.1 Generalized Fractal Strings; 4.1.1 Examples of Generalized Fractal Strings; 4.2 The Frequencies of a Generalized Fractal String , 4.2.1 Completion of the Harmonic String: Euler Product4.3 Generalized Fractal Sprays; 4.4 The Measure of a Self-Similar String; 4.4.1 Measures with a Self-Similarity Property; 4.5 Notes; 5 Explicit Formulas for Generalized Fractal Strings; 5.1 Introduction; 5.1.1 Outline of the Proof; 5.1.2 Examples; 5.2 Preliminaries: The Heaviside Function; 5.3 Pointwise Explicit Formulas; 5.3.1 The Order of Growth of the Sum over the Complex Dimensions; 5.4 Distributional Explicit Formulas; 5.4.1 Extension to More General Test Functions; 5.4.2 The Order of the Distributional Error Term , 5.5 Example: The Prime Number Theorem

Weitere Ausg.: ISBN 9781461421757

Weitere Ausg.: Buchausg. u.d.T. Lapidus, Michel L., 1956 - Fractal geometry, complex dimensions and zeta functions New York, NY : Springer, 2013 ISBN 9781461421757

Weitere Ausg.: ISBN 9781489988386

Sprache: Englisch

Fachgebiete: Mathematik

Schlagwort(e): Zetafunktion ; Geometrische Maßtheorie ; Fraktal ; Asymptotische Verteilung ; Partielle Differentialgleichung ; Zetafunktion ; Geometrische Maßtheorie ; Fraktal ; Asymptotische Verteilung ; Partielle Differentialgleichung ; Fraktalgeometrie ; Bibliografie

DOI: 10.1007/978-1-4614-2176-4

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Mehr zum Autor: Frankenhuysen, Machiel van 1967-

Mehr zum Autor: Lapidus, Michel L. 1956-

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Umfang: 1 Online-Ressource.

Ausgabe: Völlig neu bearbeitete Ausgabe / herausgegeben von Helmut Holzhey

Anmerkung: Volltext Datenbank. - Ab 2019 herausgegeben von Laurent Cesalli und Gerald Hartung

Weitere Ausg.: Erscheint auch als Druck-Ausgabe

Sprache: Deutsch

Fachgebiete: Theologie/Religionswissenschaften , Philosophie , Altertumswissenschaften

Schlagwort(e): Philosophie ; Bibliografie ; Datenbank

DOI: 10.24894/Grundriss

URL: Volltext  (URL des Erstveröffentlichers)

Mehr zum Autor: Holzhey, Helmut 1937-

Mehr zum Autor: Cesalli, Laurent 1968-

Mehr zum Autor: Hartung, Gerald 1963-

Mehr zum Autor: Ueberweg, Friedrich 1826-1871