Elliptic Curves And Arithmetic Invariants
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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.
The Computational And Theoretical Aspects Of Elliptic Curves
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Author : Zhibin Liang
language : en
Publisher: Springer
Release Date : 2019-05-22
The Computational And Theoretical Aspects Of Elliptic Curves written by Zhibin Liang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-22 with Mathematics categories.
This volume presents a collection of results related to the BSD conjecture, based on the first two India-China conferences on this topic. It provides an overview of the conjecture and a few special cases where the conjecture is proved. The broad theme of the two conferences was “Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture”. The first was held at Beijing International Centre for Mathematical Research (BICMR) in December 2014 and the second was held at the International Centre for Theoretical Sciences (ICTS), Bangalore, India in December 2016. Providing a broad overview of the subject, the book is a valuable resource for young researchers wishing to work in this area. The articles have an extensive list of references to enable diligent researchers to gain an idea of the current state of art on this conjecture.
Elliptic Curves
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Author : Henry McKean
language : en
Publisher: Cambridge University Press
Release Date : 1999-08-13
Elliptic Curves written by Henry McKean and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-08-13 with Mathematics categories.
The subject of elliptic curves is one of the jewels of nineteenth-century mathematics, originated by Abel, Gauss, Jacobi, and Legendre. This 1997 book presents an introductory account of the subject in the style of the original discoverers, with references to and comments about more recent and modern developments. It combines three of the fundamental themes of mathematics: complex function theory, geometry, and arithmetic. After an informal preparatory chapter, the book follows an historical path, beginning with the work of Abel and Gauss on elliptic integrals and elliptic functions. This is followed by chapters on theta functions, modular groups and modular functions, the quintic, the imaginary quadratic field, and on elliptic curves. Requiring only a first acquaintance with complex function theory, this book is an ideal introduction to the subject for graduate students and researchers in mathematics and physics, with many exercises with hints scattered throughout the text.
Elliptic Functions
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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Elliptic Functions written by Serge Lang 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 2012-12-06 with Mathematics categories.
Elliptic functions parametrize elliptic curves, and the intermingling of the analytic and algebraic-arithmetic theory has been at the center of mathematics since the early part of the nineteenth century. The book is divided into four parts. In the first, Lang presents the general analytic theory starting from scratch. Most of this can be read by a student with a basic knowledge of complex analysis. The next part treats complex multiplication, including a discussion of Deuring's theory of l-adic and p-adic representations, and elliptic curves with singular invariants. Part three covers curves with non-integral invariants, and applies the Tate parametrization to give Serre's results on division points. The last part covers theta functions and the Kronecker Limit Formula. Also included is an appendix by Tate on algebraic formulas in arbitrary charactistic.
Elliptic Curves
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Author : Dale Husemoller
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Elliptic Curves written by Dale Husemoller 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 2013-06-29 with Mathematics categories.
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.
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 In Cryptography
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Author : Ian F. Blake
language : en
Publisher: Cambridge University Press
Release Date : 1999-07-08
Elliptic Curves In Cryptography written by Ian F. Blake and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-07-08 with Computers categories.
This book summarizes knowledge built up within Hewlett-Packard over a number of years, and explains the mathematics behind practical implementations of elliptic curve systems. Due to the advanced nature of the mathematics there is a high barrier to entry for individuals and companies to this technology. Hence this book will be invaluable not only to mathematicians wanting to see how pure mathematics can be applied but also to engineers and computer scientists wishing (or needing) to actually implement such systems.
Proceedings Of The Seventh International Conference On Mathematics And Computing
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Author : Debasis Giri
language : en
Publisher: Springer Nature
Release Date : 2022-03-05
Proceedings Of The Seventh International Conference On Mathematics And Computing written by Debasis Giri and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-05 with Technology & Engineering categories.
This book features selected papers from the 7th International Conference on Mathematics and Computing (ICMC 2021), organized by Indian Institute of Engineering Science and Technology (IIEST), Shibpur, India, during March 2021. It covers recent advances in the field of mathematics, statistics, and scientific computing. The book presents innovative work by leading academics, researchers, and experts from industry.
Algorithmic Number Theory
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Author : Florian Hess
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-07-06
Algorithmic Number Theory written by Florian Hess 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 2006-07-06 with Computers categories.
This book constitutes the refereed proceedings of the 7th International Algorithmic Number Theory Symposium, ANTS 2006, held in Berlin, Germany in July 2006. The 37 revised full papers presented together with 4 invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on algebraic number theory, analytic and elementary number theory, lattices, curves and varieties over fields of characteristic zero, curves over finite fields and applications, and discrete logarithms.
Number Theory
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Author : W.A. Coppel
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-03
Number Theory written by W.A. Coppel 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 2009-10-03 with Mathematics categories.
Number Theory is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and discrete mathematics are all included. The book is divided into two parts. Part A covers key concepts of number theory and could serve as a first course on the subject. Part B delves into more advanced topics and an exploration of related mathematics. The prerequisites for this self-contained text are elements from linear algebra. Valuable references for the reader are collected at the end of each chapter. It is suitable as an introduction to higher level mathematics for undergraduates, or for self-study.