Download or read book Borcherds Products on O 2 l and Chern Classes of Heegner Divisors written by Jan H. Bruinier and published by Springer. This book was released on 2004-10-11 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: Around 1994 R. Borcherds discovered a new type of meromorphic modular form on the orthogonal group $O(2,n)$. These "Borcherds products" have infinite product expansions analogous to the Dedekind eta-function. They arise as multiplicative liftings of elliptic modular forms on $(SL)_2(R)$. The fact that the zeros and poles of Borcherds products are explicitly given in terms of Heegner divisors makes them interesting for geometric and arithmetic applications. In the present text the Borcherds' construction is extended to Maass wave forms and is used to study the Chern classes of Heegner divisors. A converse theorem for the lifting is proved.
Download or read book L Functions and Automorphic Forms written by Jan Hendrik Bruinier and published by Springer. This book was released on 2018-02-22 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of carefully refereed research articles and lecture notes stemming from the Conference "Automorphic Forms and L-Functions", held at the University of Heidelberg in 2016. The theory of automorphic forms and their associated L-functions is one of the central research areas in modern number theory, linking number theory, arithmetic geometry, representation theory, and complex analysis in many profound ways. The 19 papers cover a wide range of topics within the scope of the conference, including automorphic L-functions and their special values, p-adic modular forms, Eisenstein series, Borcherds products, automorphic periods, and many more.
Download or read book Geometry and Analysis of Automorphic Forms of Several Variables written by Yoshinori Hamahata and published by World Scientific. This book was released on 2012 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains contributions of principal speakers of the symposium on geometry and analysis of automorphic forms of several variables, held in September 2009 at Tokyo, Japan, in honor of Takayuki Oda''s 60th birthday. It presents both research and survey articles in the fields that are the main themes of his work. The volume may serve as a guide to developing areas as well as a resource for researchers who seek a broader view and for students who are beginning to explore automorphic form.
Download or read book Automorphic Forms written by Bernhard Heim and published by Springer. This book was released on 2014-11-19 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume presents a collection of carefully refereed articles covering the latest advances in Automorphic Forms and Number Theory, that were primarily developed from presentations given at the 2012 “International Conference on Automorphic Forms and Number Theory,” held in Muscat, Sultanate of Oman. The present volume includes original research as well as some surveys and outlines of research altogether providing a contemporary snapshot on the latest activities in the field and covering the topics of: Borcherds products Congruences and Codes Jacobi forms Siegel and Hermitian modular forms Special values of L-series Recently, the Sultanate of Oman became a member of the International Mathematical Society. In view of this development, the conference provided the platform for scientific exchange and collaboration between scientists of different countries from all over the world. In particular, an opportunity was established for a close exchange between scientists and students of Germany, Oman, and Japan. The conference was hosted by the Sultan Qaboos University and the German University of Technology in Oman.
Download or read book Partition Functions and Automorphic Forms written by Valery A. Gritsenko and published by Springer Nature. This book was released on 2020-07-09 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to the research in several recently discovered and actively developing mathematical and mathematical physics areas. It focuses on: 1) Feynman integrals and modular functions, 2) hyperbolic and Lorentzian Kac-Moody algebras, related automorphic forms and applications to quantum gravity, 3) superconformal indices and elliptic hypergeometric integrals, related instanton partition functions, 4) moonshine, its arithmetic aspects, Jacobi forms, elliptic genus, and string theory, and 5) theory and applications of the elliptic Painleve equation, and aspects of Painleve equations in quantum field theories. All the topics covered are related to various partition functions emerging in different supersymmetric and ordinary quantum field theories in curved space-times of different (d=2,3,...,6) dimensions. Presenting multidisciplinary methods (localization, Borcherds products, theory of special functions, Cremona maps, etc) for treating a range of partition functions, the book is intended for graduate students and young postdocs interested in the interaction between quantum field theory and mathematics related to automorphic forms, representation theory, number theory and geometry, and mirror symmetry.
Download or read book Mathematisches Institut Georg august universit t G ttingen Seminars Summer 2003 2004 written by Yuri Tschinkel and published by Universitätsverlag Göttingen. This book was released on 2004 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains lecture notes from the seminars [alpha]Number Theory", [alpha]Algebraic Geometry" and [alpha]Geometric methods in representation theory" which took place at the Mathematics Institute of the University of Göttingen during the Winter Term 2003-2004. Most contributions report on recent work by the authors.
Download or read book Partitions q Series and Modular Forms written by Krishnaswami Alladi and published by Springer Science & Business Media. This book was released on 2011-11-01 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Partitions, q-Series, and Modular Forms contains a collection of research and survey papers that grew out of a Conference on Partitions, q-Series and Modular Forms at the University of Florida, Gainesville in March 2008. It will be of interest to researchers and graduate students that would like to learn of recent developments in the theory of q-series and modular and how it relates to number theory, combinatorics and special functions.
Download or read book Moonshine The First Quarter Century and Beyond written by James Lepowsky and published by Cambridge University Press. This book was released on 2010-06-03 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume examines the impact of the 'Monstrous Moonshine' paper on mathematics and theoretical physics.
Download or read book Dynamical Systems Number Theory and Applications written by Thomas Hagen and published by World Scientific. This book was released on 2016-01-25 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of a selection of research-type articles on dynamical systems, evolution equations, analytic number theory and closely related topics. A strong emphasis is on a fair balance between theoretical and more applied work, thus spanning the chasm between abstract insight and actual application. Several of the articles are expected to be in the intersection of dynamical systems theory and number theory. One article will likely relate the topics presented to the academic achievements and interests of Prof. Leutbecher and shed light on common threads among all the contributions. Contents:PrefaceBiographical Note on Armin Leutbecher (S Walcher)Das Jahr 1934 ... (J Fischer)Explicit Expressions for Equivariant Minimal Lagrangian Surfaces (J F Dorfmeister & H Ma)Rational Parameter Rays of the Multibrot Sets (D Eberlein, S Mukherjee & D Schleicher)The Matovich-Pearson Equations Revisited (T Hagen)Diffeomorphisms with Stable Manifolds as Basin Boundaries (S Hayes & Ch Wolf)A New Type of Functional Equations of Euler Products (B Heim)The Hexagonal Lattice and the Epstein Zeta Function (A Henn)On Putative q-Analogues of the Fano Plane (Th Honold & M Kiermaier)Integral Orthogonal Groups (A Krieg)The Role of Fourier Analysis in X-Ray Crystallography (F Rupp & J Scheurle)An Elementary Proof for Joint Continuity of Semiflows (S Schmitz)A Convergent String Method (H Schwetlick & J Zimmer)Variational Symmetries and Pluri-Lagrangian Systems (Y B Suris) Readership: Researchers in algebra and number theory, dynamical systems and analysis and differential equations. Key Features:This versatile book covers state-of-the art work in dynamical systems, analytic number theory and applied analysisIt appeals to a wide audience due to its broad range of topics, highlighting both the breadth and the depth of modern analytical work without losing sight of a common coreKeywords:Dynamical Systems;Evolution Equations;Number Theory;Differential Geometry
Download or read book The 1 2 3 of Modular Forms written by Jan Hendrik Bruinier and published by Springer Science & Business Media. This book was released on 2008-02-10 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.
Download or read book Arithmetic and Geometry written by Luis Dieulefait and published by Cambridge University Press. This book was released on 2015-10-08 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The 'Arithmetic and Geometry' trimester, held at the Hausdorff Research Institute for Mathematics in Bonn, focussed on recent work on Serre's conjecture and on rational points on algebraic varieties. The resulting proceedings volume provides a modern overview of the subject for graduate students in arithmetic geometry and Diophantine geometry. It is also essential reading for any researcher wishing to keep abreast of the latest developments in the field. Highlights include Tim Browning's survey on applications of the circle method to rational points on algebraic varieties and Per Salberger's chapter on rational points on cubic hypersurfaces.
Download or read book The Geometric and Arithmetic Volume of Shimura Varieties of Orthogonal Type written by Fritz Hörmann and published by American Mathematical Society. This book was released on 2014-11-05 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book outlines a functorial theory of integral models of (mixed) Shimura varieties and of their toroidal compactifications, for odd primes of good reduction. This is the integral version, developed in the author's thesis, of the theory invented by Deligne and Pink in the rational case. In addition, the author develops a theory of arithmetic Chern classes of integral automorphic vector bundles with singular metrics using the work of Burgos, Kramer and Kühn. The main application is calculating arithmetic volumes or "heights" of Shimura varieties of orthogonal type using Borcherds' famous modular forms with their striking product formula--an idea due to Bruinier-Burgos-Kühn and Kudla. This should be seen as an Arakelov analogue of the classical calculation of volumes of orthogonal locally symmetric spaces by Siegel and Weil. In the latter theory, the volumes are related to special values of (normalized) Siegel Eisenstein series. In this book, it is proved that the Arakelov analogues are related to special derivatives of such Eisenstein series. This result gives substantial evidence in the direction of Kudla's conjectures in arbitrary dimensions. The validity of the full set of conjectures of Kudla, in turn, would give a conceptual proof and far-reaching generalizations of the work of Gross and Zagier on the Birch and Swinnerton-Dyer conjecture. Titles in this series are co-published with the Centre de Recherches Mathématiques.
Download or read book Number Theory and Modular Forms written by Bruce C. Berndt and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robert A. Rankin, one of the world's foremost authorities on modular forms and a founding editor of The Ramanujan Journal, died on January 27, 2001, at the age of 85. Rankin had broad interests and contributed fundamental papers in a wide variety of areas within number theory, geometry, analysis, and algebra. To commemorate Rankin's life and work, the editors have collected together 25 papers by several eminent mathematicians reflecting Rankin's extensive range of interests within number theory. Many of these papers reflect Rankin's primary focus in modular forms. It is the editors' fervent hope that mathematicians will be stimulated by these papers and gain a greater appreciation for Rankin's contributions to mathematics. This volume would be an inspiration to students and researchers in the areas of number theory and modular forms.
Download or read book Developments and Trends in Infinite Dimensional Lie Theory written by Karl-Hermann Neeb and published by Springer Science & Business Media. This book was released on 2010-10-17 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups. Contributors: B. Allison, D. Beltiţă, W. Bertram, J. Faulkner, Ph. Gille, H. Glöckner, K.-H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf.
Download or read book Analytic Number Theory Modular Forms and q Hypergeometric Series written by George E. Andrews and published by Springer. This book was released on 2018-02-01 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gathered from the 2016 Gainesville Number Theory Conference honoring Krishna Alladi on his 60th birthday, these proceedings present recent research in number theory. Extensive and detailed, this volume features 40 articles by leading researchers on topics in analytic number theory, probabilistic number theory, irrationality and transcendence, Diophantine analysis, partitions, basic hypergeometric series, and modular forms. Readers will also find detailed discussions of several aspects of the path-breaking work of Srinivasa Ramanujan and its influence on current research. Many of the papers were motivated by Alladi's own research on partitions and q-series as well as his earlier work in number theory. Alladi is well known for his contributions in number theory and mathematics. His research interests include combinatorics, discrete mathematics, sieve methods, probabilistic and analytic number theory, Diophantine approximations, partitions and q-series identities. Graduate students and researchers will find this volume a valuable resource on new developments in various aspects of number theory.
Download or read book Punctured Torus Groups and 2 Bridge Knot Groups I written by Hirotaka Akiyoshi and published by Springer. This book was released on 2007-05-26 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is the first part of a work that provides a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization. It offers an elementary and self-contained description of Jorgensen's theory with a complete proof. Through various informative illustrations, readers are naturally led to an intuitive, synthetic grasp of the theory, which clarifies how a very simple fuchsian group evolves into complicated Kleinian groups.
Download or read book Algebraic Groups and Lie Groups with Few Factors written by Alfonso Di Bartolo and published by Springer. This book was released on 2008-04-03 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic groups are treated in this volume from a group theoretical point of view and the obtained results are compared with the analogous issues in the theory of Lie groups. The main body of the text is devoted to a classification of algebraic groups and Lie groups having only few subgroups or few factor groups of different type. In particular, the diversity of the nature of algebraic groups over fields of positive characteristic and over fields of characteristic zero is emphasized. This is revealed by the plethora of three-dimensional unipotent algebraic groups over a perfect field of positive characteristic, as well as, by many concrete examples which cover an area systematically. In the final section, algebraic groups and Lie groups having many closed normal subgroups are determined.
