Euler Systems And Arithmetic Applications
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Euler Systems And Arithmetic Applications
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Author : Andrew Graham
language : en
Publisher:
Release Date : 2021
Euler Systems And Arithmetic Applications written by Andrew Graham and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
Euler Systems
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Author : Karl Rubin
language : en
Publisher: Princeton University Press
Release Date : 2000-05-21
Euler Systems written by Karl Rubin and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-05-21 with Mathematics categories.
One of the most exciting new subjects in Algebraic Number Theory and Arithmetic Algebraic Geometry is the theory of Euler systems. Euler systems are special collections of cohomology classes attached to p-adic Galois representations. Introduced by Victor Kolyvagin in the late 1980s in order to bound Selmer groups attached to p-adic representations, Euler systems have since been used to solve several key problems. These include certain cases of the Birch and Swinnerton-Dyer Conjecture and the Main Conjecture of Iwasawa Theory. Because Selmer groups play a central role in Arithmetic Algebraic Geometry, Euler systems should be a powerful tool in the future development of the field. Here, in the first book to appear on the subject, Karl Rubin presents a self-contained development of the theory of Euler systems. Rubin first reviews and develops the necessary facts from Galois cohomology. He then introduces Euler systems, states the main theorems, and develops examples and applications. The remainder of the book is devoted to the proofs of the main theorems as well as some further speculations. The book assumes a solid background in algebraic Number Theory, and is suitable as an advanced graduate text. As a research monograph it will also prove useful to number theorists and researchers in Arithmetic Algebraic Geometry.
Geometry And Arithmetic Around Euler Partial Differential Equations
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Author : R.-P. Holzapfel
language : en
Publisher: Springer
Release Date : 1986-08-31
Geometry And Arithmetic Around Euler Partial Differential Equations written by R.-P. Holzapfel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-08-31 with Mathematics categories.
On Boundary Regularity Of Vortex Patches For 3d Incompressible Euler Systems
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Author : University of Minnesota. Institute for Mathematics and Its Applications
language : en
Publisher:
Release Date : 1996
On Boundary Regularity Of Vortex Patches For 3d Incompressible Euler Systems written by University of Minnesota. Institute for Mathematics and Its Applications and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
Fundamental Number Theory With Applications
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Author : Richard A. Mollin
language : en
Publisher: CRC Press
Release Date : 2008-02-21
Fundamental Number Theory With Applications written by Richard A. Mollin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-21 with Mathematics categories.
An update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. The substantial amount of reorganizing makes this edition clearer and more elementary in its coverage. New to the Second Edition • Removal of all advanced material to be even more accessible in scope • New fundamental material, including partition theory, generating functions, and combinatorial number theory • Expanded coverage of random number generation, Diophantine analysis, and additive number theory • More applications to cryptography, primality testing, and factoring • An appendix on the recently discovered unconditional deterministic polynomial-time algorithm for primality testing Taking a truly elementary approach to number theory, this text supplies the essential material for a first course on the subject. Placed in highlighted boxes to reduce distraction from the main text, nearly 70 biographies focus on major contributors to the field. The presentation of over 1,300 entries in the index maximizes cross-referencing so students can find data with ease.
Number Theory And Applications
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Author : S.D. Adhikari
language : en
Publisher: Springer
Release Date : 2009-06-15
Number Theory And Applications written by S.D. Adhikari and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-15 with Mathematics categories.
This collection of articles contains the proceedings of the two international conferences (on Number Theory and Cryptography) held at the Harish - Chandra Research Institute. In recent years the interest in number theory has increased due to its applications in areas like error-correcting codes and cryptography. These proceedings contain papers in various areas of number theory, such as combinatorial, algebraic, analytic and transcendental aspects, arithmetic algebraic geometry, as well as graph theory and cryptography. While some papers do contain new results, several of the papers are expository articles that mention open questions, which will be useful to young researchers.
Hyperbolic Problems
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Author : Song Jiang
language : en
Publisher: World Scientific
Release Date : 2012
Hyperbolic Problems written by Song Jiang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
This two-volume book is devoted to mathematical theory, numerics and applications of hyperbolic problems. Hyperbolic problems have not only a long history but also extremely rich physical background. The development is highly stimulated by their applications to Physics, Biology, and Engineering Sciences; in particular, by the design of effective numerical algorithms. Due to recent rapid development of computers, more and more scientists use hyperbolic partial differential equations and related evolutionary equations as basic tools when proposing new mathematical models of various phenomena and related numerical algorithms.This book contains 80 original research and review papers which are written by leading researchers and promising young scientists, which cover a diverse range of multi-disciplinary topics addressing theoretical, modeling and computational issues arising under the umbrella of OC Hyperbolic Partial Differential EquationsOCO. It is aimed at mathematicians, researchers in applied sciences and graduate students."
Kolyvagin Systems
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Author : Barry Mazur
language : en
Publisher: Amer Mathematical Society
Release Date : 2004
Kolyvagin Systems written by Barry Mazur and has been published by Amer Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Since their introduction by Kolyvagin, Euler systems have been used in several important applications in arithmetic algebraic geometry. For a $p$-adic Galois module $T$, Kolyvagin's machinery is designed to provide an upper bound for the size of the Selmer group associated to the Cartier dual $T^*$. Given an Euler system, Kolyvagin produces a collection of cohomology classes which he calls ``derivative'' classes. It is these derivative classes which are used to bound the dual Selmer group. The starting point of the present memoir is the observation that Kolyvagin's systems of derivative classes satisfy stronger interrelations than have previously been recognized. We call a system of cohomology classes satisfying these stronger interrelations a Kolyvagin system. We show that the extra interrelations give Kolyvagin systems an interesting rigid structure which in many ways resembles (an enriched version of) the ``leading term'' of an $L$-function. By making use of the extra rigidity we also prove that Kolyvagin systems exist for many interesting representations for which no Euler system is known, and further that there are Kolyvagin systems for these representations which give rise to exact formulas for the size of the dual Selmer group, rather than just upper bounds.
Introduction To Number Theory
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Author : Martin Erickson
language : en
Publisher: Chapman and Hall/CRC
Release Date : 2008
Introduction To Number Theory written by Martin Erickson and has been published by Chapman and Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Computers categories.
One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topics. This classroom-tested, student-friendly text covers a wide range of subjects, from the ancient Euclidean algorithm for finding the greatest common divisor of two integers to recent developments that include cryptography, the theory of elliptic curves, and the negative solution of Hilbert’s tenth problem. The authors illustrate the connections between number theory and other areas of mathematics, including algebra, analysis, and combinatorics. They also describe applications of number theory to real-world problems, such as congruences in the ISBN system, modular arithmetic and Euler’s theorem in RSA encryption, and quadratic residues in the construction of tournaments. The book interweaves the theoretical development of the material with Mathematica® and MapleTM calculations while giving brief tutorials on the software in the appendices. Highlighting both fundamental and advanced topics, this introduction provides all of the tools to achieve a solid foundation in number theory.
Number Theory For Computing
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Author : Song Y. Yan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Number Theory For Computing written by Song Y. Yan 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 2013-11-11 with Computers categories.
This book provides a good introduction to the classical elementary number theory and the modern algorithmic number theory, and their applications in computing and information technology, including computer systems design, cryptography and network security. In this second edition proofs of many theorems have been provided, further additions and corrections were made.