In the course of their undergraduate careers, most mathematics majors see little beyond standard mathematics. In conclusion, i recommend this book to the set of people interested in p adic numbers, and its complement. Introduction to p adic analytic number theory download. Gouvea, 9783540629115, available at book depository with free delivery worldwide. The aim of the first chapter of this book is to introduce its main protagonist. To my eyes, the most glaring omission was a book by fernando gouvea, originally published in, entitled padic numbers. In particular, p adic numbers are considered to be close. Further, they offer a realm where one can do things that are very similar to classical analysis, but with results that are quite unusual.
Serif fand mare p adic or overconvergent versions of the same thing. Here i do not demand the applications to be purely mathematical. Dec 06, 2012 over the last century, p adic numbers and p adic analysis have come to playa central role in modern number theory. Lee corbin added it mar 10, there are few adventures in other territories, and few opportunities to visit some of the more exotic cor every rational has an essentially unique adic expansion essentially since zero terms can always be added at the beginning. This text is suitable for an undergrad who has taken some analysis and topology. 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 importance comes from the fact that they afford a natural and powerful language for talking about congruences between integers, and allow the use of methods borrowed from calculus and analysis for studying such problems. The third edition is in press right now and should appear in time for the fall semester.
It is perhaps the most suitable text for beginners, and i shall definitely recommend it to anyone who asks me. A p adic integer is a p adic number with the property that its p adic expansion satis es n 0, with n2z the starting term in the sum. It is perhaps the most suitable text for beginners, and i shall definitely recommend it to. A hints and comments on the problems this is a common argument that is used in solving these types of equations. Universitext padic numbers an introduction fernando. Gouvea my introduction to the padic numbers was last reprinted in 2003 by springerverlag. This is a common argument that is used in solving these types of equations. Peng gao rated it liked it dec 14, so we have an immediate proof of the irrationality of. This site is like a library, use search box in the widget to get ebook that you want.
The pdf files below contain versions of course notes that i have written over the past decade or so. Something i know a bit less about is katz \generalised p adic modular functions. Seventh international conference on padic in conclusion, i recommend this book to the set of people interested in padic numbers, and its complement. The reader is led into the rich structure of the fields qp and cp in a beautiful balance between analytic and algebraic aspects. The purpose of this paper is to describe the padic numbers, but so far we have only established what the padic metric is. Weyl, algebraic theory of numbers, 1940, based on lectures given in 193839 slide 15 some comments p adic methods have a long history even before kummer. Moreover, i am also interested in those applications that are partially algebraic, and yet important for some other parts of mathematics. Gouvea has succeeded admirably in taking a topic that is not standard in the undergraduate mathematics curriculum and writing a book accessible to numberrs that allows its reader to play with some. Some applications of p adic points of view to elliptic curves.
There are few adventures in other territories, and few opportunities to visit some of the more exotic cor ners of mathematics. P adic analysis compared with real, by svetlana katok is a very gentle introduction to p adic numbers. The goal of this book is to offer such an opportunity, by way of a visit. A crucial difference is that the reals form an archimedean field, while the p p adic numbers form a nonarchimedean field. In particular, if and turn out to be natural numbers, then their sum as a padic integer is no different from their sum as a natural number. Eichlinghofen, the 28th august 2015 by gilles bellot tudortmunduniversity facultyofmathematics. Weyl, algebraic theory of numbers, 1940, based on lectures given in 193839 slide 15 some comments padic methods have a long history even before kummer. It seems that hensels main motivation was the analogy between the ring of integers z, together with its. The extension is achieved by an alternative interpretation of the concept of closeness or absolute value. Mar 29, 2020 gouvea padic numbers pdf posted on march 29, 2020 by admin to my eyes, the most glaring omission was a book by fernando gouvea, originally published in, entitled padic numbers. Over the last century, p adic numbers and p adic analysis have come to playa central role in modern number theory. An introduction universitext kindle edition by gouvea, fernando quadros.
This elementary introduction offers a broad understanding of p adic numbers. The clarendon press, oxford university press, new york, 1993. A course in p adic analysis, by alain robert is a more terse and advanced book on the subject. We took advantage of this third printing of the second edition to correct a few typos. In particular, if and turn out to be natural numbers, then their sum as a p adic integer is no different from their sum as a natural number. Astm d3948 pdf for example, the equation can easily be shown to have no solutions in the field of 2 adic numbers we simply take the valuation of both sides.
I am making them available for the benefit of anyone who wishes to make use of them. For each prime number p p the ring of p p adic integers. The padic numbers are less well known than the others, but they play a fundamental role in number theory and in other parts of mathematics. The goal of this book is to offer such an opportunity, by way of a visit to the padic universe. Download it once and read it on your kindle device, pc, phones or tablets. Eichlinghofen, the 28th august 2015 by gilles bellot tudortmunduniversity. Meanwhile the theory of p adic numbers has a plenty of applications and impacts in various mathematical.
The aim of the lecture was to discuss lowlevel algorithmics for p adic numbers. In particular, two p adic numbers are considered to be close. Introduction to p adic numbers an overview of ultrametric spaces and p adic numbers. The set of all p adic integers will be noted as z p whereas that of all p adic numbers will be noted as q p with p2p. Seventh international conference on p adic in conclusion, i recommend this book to the set of people interested in p adic numbers, and its complement. Proceedings of the third conference of the canadian number theory association held at queens university, kingston, ontario, august 1824, 1991. Click download or read online button to get introduction to p adic analytic number theory book now.
The goal of this book is to offer such an opportunity, by way of a visit to the p adic universe. You can tell whether you have the new printing because this one has my photo on the back cover. Hensel though they are foreshadowed in the work of his predecessor e. For people who prefer an algebraic approach, one can also define the p adic integers as an inverse limit of the rings zp n z and then define the p adic rational numbers as the fraction field of this inverse limit. Important applications of padic numbers outside of algebra. Use features like bookmarks, note taking and highlighting while reading padic numbers. Please let me know if you find them useful or otherwise and let me know of any. In mathematics, the p adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems. Sep 17, 2019 gouvea padic numbers pdf september 17, 2019 admin history leave a comment on gouvea padic numbers pdf to my eyes, the most glaring omission was a book by fernando gouvea, originally published in, entitled padic numbers. Use features like bookmarks, note taking and highlighting while reading p adic numbers. An introduction came out in mid2003, so it was more than time to revamp it. May 22, 2003 over the last century, p adic numbers and p adic analysis have come to playa central role in modern number theory.
The p adic rational numbers are then the completion of the rational numbers with respect to this absolute value. Before we can ask why q p is important, we must ask why these new metrics one for each prime p are important. They have some things in common with usual numbers and they include the rational numbers math\mathbf qmath. An introduction to p adic numbers and p adic analysis.
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