to the p-adic number system as far as its metric and properties are concerned. . cation “p-adic Numbers: An Introduction”, by Fernando Q. Gouvêa. Proposition. () The p-adic numbers were first p n for a, b, n ∈ Z, where the prime p divides neither a nor b. p-adic norm . Fernando Q. Gouvea. p-adic Numbers, An . To my eyes, the most glaring omission was a book by Fernando Gouvêa, originally published in , entitled p-adic Numbers: An Introduction.

p-adic Numbers: An Introduction – Fernando Gouvea – Google Books

gouves There are two things I love in particular: By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

Edgar De marked it as to-read Nov 04, Elementary Analysis in Qp Yet another application is provided by the Mahler-Lech theorem. The -adics were probably first introduced by Hensel in a paper which was concerned with the development of algebraic numbers in power series. Algebraic Numbers and Functions. Hasse subsequently formulated the Hasse principlewhich is one of the chief applications of local field theory. This edition, co-published by Oxton House and the Mathematical Association of Americaaims to satisfy those requests.

Want to Read Currently Reading Read. The goal of this book is to offer such an opportunity, by way of a visit to the p-adic universe. In language mathematicians will find familiar, this means all the ideas are motivated, but it goes beyond that.

If you need to see me at a different time, please email me to make an appointment. I find such problems very very difficult to get motivated by. Here is the full list. Thanks for that, especially the answer on my second question was very useful. You already told me what the answer is! 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.

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. Practice online or make a printable study sheet.

Thiago Dourado marked it as to-read Dec 15, Note that I am almost never on campus on Thursdays. This is a common argument that is used in solving these types of equations: Joao Alberto de Faria rated it really liked it Aug 08, This is the place to go for mathematics books: Adar marked it as to-read Jun 08, Over the last century, p-adic numbers and p-adic analysis have come to playa central role in modern number theory.

Then define the p -adic norm of by. Any nonzero rational number can be represented by.

p-adic Number

For the second edition, We added five new historical sketches on the tangent function in trigonometry, logarithms, conic sections, irrational numbers, and differential o-adic. A Gentle History for Teachers and Otherswhich I wrote together with Bill Berlinghoff, was published by Oxton House Publishers in mid, with the second edition appeared late in and in the “Expanded” version Planck Constant added it Jun 19, Apr 27 ’15 at Olivierco added it Feb 10, An Introduction Fernando Q.

Noah Lichtblau is currently reading it Oct 30, Tell all your friends! There are no proofs, but I hope readers will find it a useful overview of the material. My oguvea interests are: The completion of this space can therefore be constructed, and the set of -adic numbers is defined to be this completed space.

We have updated the rest, in some cases making fairly large changes to reflect current scholarship. I just learn better this way, there’s no doubt about it.

This elementary introduction offers a broad understanding of p-adic numbers. Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more.

Robbie added it Jan 25, gouveq There are few adventures in other territories, and few opportunities to visit some of the more exotic cor More recently, p-adic num bers have shown up in other areas of mathematics, and even in physics. Lee Corbin added it Mar 10, I really love the way Gouvea writes vouvea math. The book is an introduction to the history of mathematics with the needs of mathematics teachers chiefly in mind. Joseph Stahl rated it it was amazing Jul 07,