Download or read book Elliptic Curves MN 40 Volume 40 written by Anthony W. Knapp and published by Princeton University Press. This book was released on 2018-06-05 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group. Modular forms are analytic functions in the upper half plane with certain transformation laws and growth properties. The two subjects--elliptic curves and modular forms--come together in Eichler-Shimura theory, which constructs elliptic curves out of modular forms of a special kind. The converse, that all rational elliptic curves arise this way, is called the Taniyama-Weil Conjecture and is known to imply Fermat's Last Theorem. Elliptic curves and the modeular forms in the Eichler- Shimura theory both have associated L functions, and it is a consequence of the theory that the two kinds of L functions match. The theory covered by Anthony Knapp in this book is, therefore, a window into a broad expanse of mathematics--including class field theory, arithmetic algebraic geometry, and group representations--in which the concidence of L functions relates analysis and algebra in the most fundamental ways. Developing, with many examples, the elementary theory of elliptic curves, the book goes on to the subject of modular forms and the first connections with elliptic curves. The last two chapters concern Eichler-Shimura theory, which establishes a much deeper relationship between the two subjects. No other book in print treats the basic theory of elliptic curves with only undergraduate mathematics, and no other explains Eichler-Shimura theory in such an accessible manner.
Download or read book Algebraic Geometry II Cohomology of Schemes written by Ulrich Görtz and published by Springer Nature. This book was released on 2023-11-22 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book completes the comprehensive introduction to modern algebraic geometry which was started with the introductory volume Algebraic Geometry I: Schemes. It begins by discussing in detail the notions of smooth, unramified and étale morphisms including the étale fundamental group. The main part is dedicated to the cohomology of quasi-coherent sheaves. The treatment is based on the formalism of derived categories which allows an efficient and conceptual treatment of the theory, which is of crucial importance in all areas of algebraic geometry. After the foundations are set up, several more advanced topics are studied, such as numerical intersection theory, an abstract version of the Theorem of Grothendieck-Riemann-Roch, the Theorem on Formal Functions, Grothendieck's algebraization results and a very general version of Grothendieck duality. The book concludes with chapters on curves and on abelian schemes, which serve to develop the basics of the theory of these two important classes of schemes on an advanced level, and at the same time to illustrate the power of the techniques introduced previously. The text contains many exercises that allow the reader to check their comprehension of the text, present further examples or give an outlook on further results.
Download or read book Elliptic Curves written by Dale Husemoller and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book divides naturally into several parts according to the level of the material, the background required of the reader, and the style of presentation with respect to details of proofs. For example, the first part, to Chapter 6, is undergraduate in level, the second part requires a background in Galois theory and the third some complex analysis, while the last parts, from Chapter 12 on, are mostly at graduate level. A general outline ofmuch ofthe material can be found in Tate's colloquium lectures reproduced as an article in Inven tiones [1974]. The first part grew out of Tate's 1961 Haverford Philips Lectures as an attempt to write something for publication c10sely related to the original Tate notes which were more or less taken from the tape recording of the lectures themselves. This inc1udes parts of the Introduction and the first six chapters The aim ofthis part is to prove, by elementary methods, the Mordell theorem on the finite generation of the rational points on elliptic curves defined over the rational numbers. In 1970 Tate teturned to Haverford to give again, in revised form, the originallectures of 1961 and to extend the material so that it would be suitable for publication. This led to a broader plan forthe book.
Download or read book Arithmetic moduli of elliptic curves written by Nicholas M. Katz and published by . This book was released on 1985 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Abelian l Adic Representations and Elliptic Curves written by Jean-Pierre Serre and published by CRC Press. This book was released on 1997-11-15 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat's Last Theorem. The initial chapters are devoted to the Abelian case (complex multiplication), where one
Download or read book Advances in Cryptology ASIACRYPT 2012 written by Xiaoyun Wang and published by Springer Science & Business Media. This book was released on 2012-11-19 with total page 791 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 18th International Conference on the Theory and Application of Cryptology and Information Security, Asiacrypt 2012, held in Beijing, China, in December 2012. The 43 full papers presented were carefully reviewed and selected from 241 submissions. They are organized in topical sections named: public-key cryptography, foundation, symmetric cipher, security proof, lattice-based cryptography and number theory, hash function, cryptographic protocol, and implementation issues.
Download or read book Diophantine m tuples and Elliptic Curves written by Andrej Dujella and published by Springer Nature. This book was released on with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advances in Cryptology EUROCRYPT 2013 written by Thomas Johansson and published by Springer. This book was released on 2013-05-09 with total page 749 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2013, held in Athens, Greece, in May 2013. The 41 full papers included in this volume were carefully reviewed and selected from 201 submissions. They deal with cryptanalysis of hash functions, side-channel attacks, number theory, lattices, public key encryption, digital signatures, homomorphic cryptography, quantum cryptography, storage, tools, and secure computation.
Download or read book The Fundamental Critical Points of Modular Elliptic Curves written by Jack Fearnley and published by . This book was released on 1996 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In their paper, "Arithmetic of Weil Curves", Mazur and Swinnerton-Dyer prove that the number of fundamental critical points of the normalized weight two modular form associated with an elliptic curve is an upper bound on the analytic rank of the curve. Their calculation of this quantity for all elliptic curves of conductor less than 424 confirmed that, with only 16 exceptions, the bound is sharp. It is the intention of this thesis to compute the number of fundamental critical points for all curves of conductor less than 4000.
Download or read book The Bulletin of Mathematics Books written by and published by . This book was released on 1992 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Arithmetic of Elliptic Curves written by Joseph H. Silverman and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.
Download or read book Information Security written by Kan Zhang and published by Springer Science & Business Media. This book was released on 2004-09-17 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 7th International Information Security Conference, ISC 2004, held in Palo Alto, CA, USA, in September 2004. The 36 revised full papers presented were carefully reviewed and selected from 106 submissions. The papers are organized in topical sections on key management, digital signatures, new algorithms, cryptanalysis, intrusion detection, access control, human authentication, certificate management, mobile and ad-hoc security, Web security, digital rights management, and software security.
Download or read book Ad Hoc Mobile and Wireless Networks written by Ioanis Nikolaidis and published by Springer Science & Business Media. This book was released on 2010-07-13 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 9th International Conference on Ad-Hoc, Mobile, and Wireless Networks, ADHOC-NOW 2010, held in Edmonton, Canada, in August 2010. The 16 revised full papers were carefully reviewed and selected from 43 submissions. The accepted papers cover topics in routing/broadcasting/multicasting protocols; energy efficiency; sensor coverage; scheduling algorithms; localization; mobility modeling; data collection and processing; and vehicular networks.
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 Topological Modular Forms written by Christopher L. Douglas and published by American Mathematical Soc.. This book was released on 2014-12-04 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of topological modular forms is an intricate blend of classical algebraic modular forms and stable homotopy groups of spheres. The construction of this theory combines an algebro-geometric perspective on elliptic curves over finite fields with techniques from algebraic topology, particularly stable homotopy theory. It has applications to and connections with manifold topology, number theory, and string theory. This book provides a careful, accessible introduction to topological modular forms. After a brief history and an extended overview of the subject, the book proper commences with an exposition of classical aspects of elliptic cohomology, including background material on elliptic curves and modular forms, a description of the moduli stack of elliptic curves, an explanation of the exact functor theorem for constructing cohomology theories, and an exploration of sheaves in stable homotopy theory. There follows a treatment of more specialized topics, including localization of spectra, the deformation theory of formal groups, and Goerss-Hopkins obstruction theory for multiplicative structures on spectra. The book then proceeds to more advanced material, including discussions of the string orientation, the sheaf of spectra on the moduli stack of elliptic curves, the homotopy of topological modular forms, and an extensive account of the construction of the spectrum of topological modular forms. The book concludes with the three original, pioneering and enormously influential manuscripts on the subject, by Hopkins, Miller, and Mahowald.
Download or read book Algorithmic Strategies for Solving Complex Problems in Cryptography written by Balasubramanian, Kannan and published by IGI Global. This book was released on 2017-08-16 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cryptography is a field that is constantly advancing, due to exponential growth in new technologies within the past few decades. Applying strategic algorithms to cryptic issues can help save time and energy in solving the expanding problems within this field. Algorithmic Strategies for Solving Complex Problems in Cryptography is an essential reference source that discusses the evolution and current trends in cryptology, and it offers new insight into how to use strategic algorithms to aid in solving intricate difficulties within this domain. Featuring relevant topics such as hash functions, homomorphic encryption schemes, two party computation, and integer factoring, this publication is ideal for academicians, graduate students, engineers, professionals, and researchers interested in expanding their knowledge of current trends and techniques within the cryptology field.
Download or read book Progress in Cryptology INDOCRYPT 2007 written by Kannan Srinathan and published by Springer Science & Business Media. This book was released on 2007-11-16 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 8th International Conference on Cryptology in India, INDOCRYPT 2007, held in Chennai, India, in December 2007. The 22 revised full papers and 11 revised short papers presented together with 3 invited lectures were carefully reviewed and selected from 104 submissions. The papers are organized in topical sections on hashing, elliptic curve, cryptoanalysis, information theoretic security, elliptic curve cryptography, signature, side channel attack, symmetric cryptosystem, asymmetric cryptosystem, and short papers.
