Elliptic Curves And Related Topics
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Advanced Topics In The Arithmetic Of Elliptic Curves
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Author : Joseph H. Silverman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Advanced Topics In The Arithmetic Of Elliptic Curves written by Joseph H. Silverman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.
The Arithmetic Of Elliptic Curves
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Author : Joseph H. Silverman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
The Arithmetic Of Elliptic Curves written by Joseph H. Silverman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
The preface to a textbook frequently contains the author's justification for offering the public "another book" on the given subject. For our chosen topic, the arithmetic of elliptic curves, there is little need for such an apologia. Considering the vast amount of research currently being done in this area, the paucity of introductory texts is somewhat surprising. Parts of the theory are contained in various books of Lang (especially [La 3] and [La 5]); and there are books of Koblitz ([Kob]) and Robert ([Rob], now out of print) which concentrate mostly on the analytic and modular theory. In addition, survey articles have been written by Cassels ([Ca 7], really a short book) and Tate ([Ta 5J, which is beautifully written, but includes no proofs). Thus the author hopes that this volume will fill a real need, both for the serious student who wishes to learn the basic facts about the arithmetic of elliptic curves; and for the research mathematician who needs a reference source for those same basic facts. Our approach is more algebraic than that taken in, say, [La 3] or [La 5], where many of the basic theorems are derived using complex analytic methods and the Lefschetz principle. For this reason, we have had to rely somewhat more on techniques from algebraic geometry. However, the geom etry of (smooth) curves, which is essentially all that we use, does not require a great deal of machinery.
Elliptic Curves
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Author : Lawrence C. Washington
language : en
Publisher: CRC Press
Release Date : 2008-04-03
Elliptic Curves written by Lawrence C. Washington and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-03 with Computers categories.
Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and application
Automorphic Forms And Related Topics
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Author : Samuele Anni
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-06-19
Automorphic Forms And Related Topics written by Samuele Anni and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-19 with Mathematics categories.
This volume contains the proceedings of the Building Bridges: 3rd EU/US Summer School and Workshop on Automorphic Forms and Related Topics, which was held in Sarajevo from July 11–22, 2016. The articles summarize material which was presented during the lectures and speed talks during the workshop. These articles address various aspects of the theory of automorphic forms and its relations with the theory of L-functions, the theory of elliptic curves, and representation theory. In addition to mathematical content, the workshop held a panel discussion on diversity and inclusion, which was chaired by a social scientist who has contributed to this volume as well. This volume is intended for researchers interested in expanding their own areas of focus, thus allowing them to “build bridges” to mathematical questions in other fields.
Elliptic Curves And Arithmetic Invariants
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Author : Haruzo Hida
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-13
Elliptic Curves And Arithmetic Invariants written by Haruzo Hida and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-13 with Mathematics categories.
This book contains a detailed account of the result of the author's recent Annals paper and JAMS paper on arithmetic invariant, including μ-invariant, L-invariant, and similar topics. This book can be regarded as an introductory text to the author's previous book p-Adic Automorphic Forms on Shimura Varieties. Written as a down-to-earth introduction to Shimura varieties, this text includes many examples and applications of the theory that provide motivation for the reader. Since it is limited to modular curves and the corresponding Shimura varieties, this book is not only a great resource for experts in the field, but it is also accessible to advanced graduate students studying number theory. Key topics include non-triviality of arithmetic invariants and special values of L-functions; elliptic curves over complex and p-adic fields; Hecke algebras; scheme theory; elliptic and modular curves over rings; and Shimura curves.
Elliptic Curves And Related Topics
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Author : H. Kisilevsky
language : en
Publisher: American Mathematical Soc.
Release Date : 1994-01-01
Elliptic Curves And Related Topics written by H. Kisilevsky and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-01 with Mathematics categories.
This book represents the proceedings of a workshop on elliptic curves held in St. Adele, Quebec, in February 1992. Containing both expository and research articles on the theory of elliptic curves, this collection covers a range of topics, from Langlands's theory to the algebraic geometry of elliptic curves, from Iwasawa theory to computational aspects of elliptic curves. This book is especially significant in that it covers topics comprising the main ingredients in Andrew Wiles's recent result on Fermat's Last Theorem.
Elliptic Curve Public Key Cryptosystems
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Author : Alfred J. Menezes
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-07-31
Elliptic Curve Public Key Cryptosystems written by Alfred J. Menezes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-07-31 with Computers categories.
Elliptic curves have been intensively studied in algebraic geometry and number theory. In recent years they have been used in devising efficient algorithms for factoring integers and primality proving, and in the construction of public key cryptosystems. Elliptic Curve Public Key Cryptosystems provides an up-to-date and self-contained treatment of elliptic curve-based public key cryptology. Elliptic curve cryptosystems potentially provide equivalent security to the existing public key schemes, but with shorter key lengths. Having short key lengths means smaller bandwidth and memory requirements and can be a crucial factor in some applications, for example the design of smart card systems. The book examines various issues which arise in the secure and efficient implementation of elliptic curve systems. Elliptic Curve Public Key Cryptosystems is a valuable reference resource for researchers in academia, government and industry who are concerned with issues of data security. Because of the comprehensive treatment, the book is also suitable for use as a text for advanced courses on the subject.
Advances On Superelliptic Curves And Their Applications
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Author : L. Beshaj
language : en
Publisher: IOS Press
Release Date : 2015-07-16
Advances On Superelliptic Curves And Their Applications written by L. Beshaj and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-16 with Computers categories.
This book had its origins in the NATO Advanced Study Institute (ASI) held in Ohrid, Macedonia, in 2014. The focus of this ASI was the arithmetic of superelliptic curves and their application in different scientific areas, including whether all the applications of hyperelliptic curves, such as cryptography, mathematical physics, quantum computation and diophantine geometry, can be carried over to the superelliptic curves. Additional papers have been added which provide some background for readers who were not at the conference, with the intention of making the book logically more complete and easier to read, but familiarity with the basic facts of algebraic geometry, commutative algebra and number theory are assumed. The book is divided into three sections. The first part deals with superelliptic curves with regard to complex numbers, the automorphisms group and the corresponding Hurwitz loci. The second part of the book focuses on the arithmetic of the subject, while the third addresses some of the applications of superelliptic curves.
Topics In Probability And Lie Groups Boundary Theory
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Author : John Christopher Taylor
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Topics In Probability And Lie Groups Boundary Theory written by John Christopher Taylor and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
This volume is comprised of two parts: the first contains articles by S. N. Evans, F. Ledrappier, and Figa-Talomanaca. These articles arose from a Centre de Recherches de Mathematiques (CRM) seminar entitiled, ``Topics in Probability on Lie Groups: Boundary Theory''. Evans gives a synthesis of his pre-1992 work on Gaussian measures on vector spaces over a local field. Ledrappier uses the freegroup on $d$ generators as a paradigm for results on the asymptotic properties of random walks and harmonic measures on the Martin boundary. These articles are followed by a case study by Figa-Talamanca using Gelfand pairs to study a diffusion on a compact ultrametric space. The second part of the book is an appendix to the book Compactifications of Symmetric Spaces (Birkhauser) by Y. Guivarc'h and J. C. Taylor. This appendix consists of an article by each author and presents the contents of this book in a more algebraic way. L. Ji and J.-P. Anker simplifies some of their results on the asymptotics of the Green function that were used to compute Martin boundaries. And Taylor gives a self-contained account of Martin boundary theory for manifolds using the theory of second order strictly elliptic partial differential operators.
Class Groups Of Number Fields And Related Topics
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Author : Kalyan Chakraborty
language : en
Publisher: Springer Nature
Release Date : 2024-12-02
Class Groups Of Number Fields And Related Topics written by Kalyan Chakraborty and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-02 with Mathematics categories.
This book collects original research papers and survey articles presented at two conferences on the same theme: the International Conference on Class Groups of Number Fields and Related Topics, held at Kerala School of Mathematics, Kozhikode, Kerala, India, from 21–24 October 2021 and then from 21–24 November 2022. It presents the fundamental research problems that arise in the study of class groups of number fields and related areas. The book also covers some new techniques and tools to study these problems. Topics in this book include class groups of number fields, units, Ankeny–Artin–Chowla conjecture, Iwasawa theory, elliptic curves, Diophantine equations, partition functions, Diophantine tuples, congruent numbers, Carmichael ideals in a number field and their connection with class groups. This book will be a valuable resource for graduate students and researchers in mathematics interested in class groups of number fields and their connections to other branches of mathematics. It also attracts new researchers to the field and young researchers will benefit immensely from the diverse problems discussed in this book. All the contributing authors are leading academicians, scientists and profound researchers. This book is dedicated to Prof. Michel Waldschmidt, a renowned French number theorist, on his 75th birthday.