P Adic Methods And Their Applications
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| 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 | : Andreĭ I︠U︡rʹevich Khrennikov |
| Publisher | : Cambridge University Press |
| Total Pages | : 255 |
| Release | : 2018-04-26 |
| Genre | : Mathematics |
| ISBN | : 1107188822 |
Provides a novel interdisciplinary perspective on the state of the art of ultrametric pseudodifferential equations and their applications.
| Author | : M. Ram Murty |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 162 |
| Release | : 2009-02-09 |
| Genre | : Mathematics |
| ISBN | : 0821847740 |
This book is an elementary introduction to $p$-adic analysis from the number theory perspective. With over 100 exercises included, it will acquaint the non-expert to the basic ideas of the theory and encourage the novice to enter this fertile field of research. The main focus of the book is the study of $p$-adic $L$-functions and their analytic properties. It begins with a basic introduction to Bernoulli numbers and continues with establishing the Kummer congruences. These congruences are then used to construct the $p$-adic analog of the Riemann zeta function and $p$-adic analogs of Dirichlet's $L$-functions. Featured is a chapter on how to apply the theory of Newton polygons to determine Galois groups of polynomials over the rational number field. As motivation for further study, the final chapter introduces Iwasawa 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 | : L. Beshaj |
| Publisher | : IOS Press |
| Total Pages | : 387 |
| Release | : 2015-07-16 |
| Genre | : Computers |
| ISBN | : 1614995206 |
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.
| Author | : Fernando Quadros Gouvea |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 304 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642590586 |
There are numbers of all kinds: rational, real, complex, p-adic. The p-adic numbers are less well known than the others, but they play a fundamental role in number theory and in other parts of mathematics. This elementary introduction offers a broad understanding of p-adic numbers. From the reviews: "It is perhaps the most suitable text for beginners, and I shall definitely recommend it to anyone who asks me what a p-adic number is." --THE MATHEMATICAL GAZETTE
| Author | : Kiran S. Kedlaya |
| Publisher | : Cambridge University Press |
| Total Pages | : 399 |
| Release | : 2010-06-10 |
| Genre | : Mathematics |
| ISBN | : 1139489208 |
Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to number theory and to computer science. This book, the first comprehensive and unified introduction to the subject, improves and simplifies existing results as well as including original material. Based on a course given by the author at MIT, this modern treatment is accessible to graduate students and researchers. Exercises are included at the end of each chapter to help the reader review the material, and the author also provides detailed references to the literature to aid further study.
| Author | : Alina Carmen Cojocaru |
| Publisher | : Cambridge University Press |
| Total Pages | : 250 |
| Release | : 2005-12-08 |
| Genre | : Mathematics |
| ISBN | : 9780521848169 |
Rather than focus on the technical details which can obscure the beauty of sieve theory, the authors focus on examples and applications, developing the theory in parallel.
| Author | : Fernando Q. Gouvêa |
| Publisher | : Springer Nature |
| Total Pages | : 366 |
| Release | : 2020-06-19 |
| Genre | : Mathematics |
| ISBN | : 3030472957 |
There are numbers of all kinds: rational, real, complex, p-adic. The p-adic numbers are less well known than the others, but they play a fundamental role in number theory and in other parts of mathematics. This elementary introduction offers a broad understanding of p-adic numbers. From the reviews: "It is perhaps the most suitable text for beginners, and I shall definitely recommend it to anyone who asks me what a p-adic number is." --THE MATHEMATICAL GAZETTE
