P Adic Methods In Number Theory And Algebraic Geometry
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| Author | : Alan Adolphson |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 254 |
| Release | : 1992 |
| Genre | : Mathematics |
| ISBN | : 0821851454 |
Two meetings of the AMS in the autumn of 1989 - one at the Stevens Institute of Technology and the other at Ball State University - included Special Sessions on the role of p-adic methods in number theory and algebraic geometry. This volume grew out of these Special Sessions. Drawn from a wide area of mathematics, the articles presented here provide an excellent sampling of the broad range of trends and applications in p-adic methods.
| Author | : Fedor Bogomolov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 365 |
| Release | : 2006-06-22 |
| Genre | : Mathematics |
| ISBN | : 0817644172 |
* Contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory * The collection gives a representative sample of problems and most recent results in algebraic and arithmetic geometry * Text can serve as an intense introduction for graduate students and those wishing to pursue research in algebraic and arithmetic geometry
| Author | : Serc Post-Doctoral Fellow Department of Mathematics Andrew J Baker |
| Publisher | : Oxford University Press on Demand |
| Total Pages | : 193 |
| Release | : 1992 |
| Genre | : Literary Criticism |
| ISBN | : 9780198535942 |
A number of texts have recently become available which provide good general introductions to p-Adic numbers and p-Adic analysis. However, there is at present a gap between such books and the sophisticated applications in the research literature. The aim of this book is to bridge this gulf byproviding a collection of intermediate level articles on various applications of p-Adic techniques throughout mathematics. The idea for producing such a volume was suggested by Oxford University Press in connection with a three day meeting `p-Adic Methods and their Applications' held at Manchester University in September 1989 and which have received financial support from the London Mathematical Society. Some of thesearticles grew out of talks given at this conference, others were written by invitation especially for this volume. All contributions were refereed with a particular view to their suitability for inclusion in such a book.
| Author | : Vasili? Sergeevich Vladimirov |
| Publisher | : World Scientific |
| Total Pages | : 350 |
| Release | : 1994 |
| Genre | : Science |
| ISBN | : 9789810208806 |
p-adic numbers play a very important role in modern number theory, algebraic geometry and representation theory. Lately p-adic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the non-Archimedean geometry of space-time at small distances.This is the first book to deal with applications of p-adic numbers in theoretical and mathematical physics. It gives an elementary and thoroughly written introduction to p-adic numbers and p-adic analysis with great numbers of examples as well as applications of p-adic numbers in classical mechanics, dynamical systems, quantum mechanics, statistical physics, quantum field theory and string theory.
| Author | : Fernando Q. Gouvea |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 285 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 3662222787 |
p-adic numbers are of great theoretical importance in number theory, since they allow the use of the language of analysis to study problems relating toprime numbers and diophantine equations. Further, they offer a realm where one can do things that are very similar to classical analysis, but with results that are quite unusual. The book should be of use to students interested in number theory, but at the same time offers an interesting example of the many connections between different parts of mathematics. The book strives to be understandable to an undergraduate audience. Very little background has been assumed, and the presentation is leisurely. There are many problems, which should help readers who are working on their own (a large appendix with hints on the problem is included). Most of all, the book should offer undergraduates exposure to some interesting mathematics which is off the beaten track. Those who will later specialize in number theory, algebraic geometry, and related subjects will benefit more directly, but all mathematics students can enjoy the book.
| Author | : Caterina Consani |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 374 |
| Release | : 2007-12-18 |
| Genre | : Mathematics |
| ISBN | : 3834803529 |
In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local L-factors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.
| Author | : Henri Cohen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 556 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 3662029456 |
A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.
| Author | : Jean Chaumine |
| Publisher | : World Scientific |
| Total Pages | : 530 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 9812793429 |
This volume covers many topics, including number theory, Boolean functions, combinatorial geometry, and algorithms over finite fields. It contains many new, theoretical and applicable results, as well as surveys that were presented by the top specialists in these areas. New results include an answer to one of Serre's questions, posted in a letter to Top; cryptographic applications of the discrete logarithm problem related to elliptic curves and hyperelliptic curves; construction of function field towers; construction of new classes of Boolean cryptographic functions; and algorithmic applications of algebraic geometry.
| Author | : Graham Everest |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 338 |
| Release | : 2015-09-03 |
| Genre | : Mathematics |
| ISBN | : 1470423154 |
Recurrence sequences are of great intrinsic interest and have been a central part of number theory for many years. Moreover, these sequences appear almost everywhere in mathematics and computer science. This book surveys the modern theory of linear recurrence sequences and their generalizations. Particular emphasis is placed on the dramatic impact that sophisticated methods from Diophantine analysis and transcendence theory have had on the subject. Related work on bilinear recurrences and an emerging connection between recurrences and graph theory are covered. Applications and links to other areas of mathematics are described, including combinatorics, dynamical systems and cryptography, and computer science. The book is suitable for researchers interested in number theory, combinatorics, and graph theory.
| Author | : Miles Reid |
| Publisher | : Cambridge University Press |
| Total Pages | : 312 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 9780521545181 |
This volume honors Sir Peter Swinnerton-Dyer's mathematical career spanning more than 60 years' of amazing creativity in number theory and algebraic geometry.
