p-adic numbers: An introduction by Fernando Quadros Gouvea

p-adic numbers: An introduction Fernando Quadros Gouvea ebook
Page: 310
Format: djvu
Publisher: Springer
ISBN: 3540629114, 9783540629115

Moving on to an analogue over the p-adic numbers due to Tate. Http: //en.wikipedia.org/wiki/P-adic_Hodge_theory The general strategy of p-adic Hodge theory, introduced by Fontaine, is to construct certain so-called period rings. You can read about this in the book 'A course in arithmetic' by J.-P. About Bruhat-Tits tree there is a nice web article titled p-Adic numbers and Bruhat-Tits tree describing also basics of p-adic numbers in a very concise form. I will try not to assume anything too number theoretic, though there won't be time to introduce the p-adic numbers in all but the briefest of detail. P(4) = 5 because 4 = 1+1+1+1 = 1+1+2 = 1+3 = 2+2 = 4. I mentioned in lecture something called the Hasse Principle, which holds for simple kinds of equations. Recently there was an intriguing breakthrough in the study of partition numbers. Partitions numbers P(n) count the number of ways of expressing n as a sum of positive integers. I highly recommend this book as an introduction to the theory of Diophantine equations with a different flavor from the present course. It occured to me that I haven't defined a p -adic number on this blog yet. The text below is this introduction in an updated form. Unit 1: Introduction to A&P 1 - 1 CHAPTER 1: AN INTRODUCTION TO A&P 1 Who will you contact if you miss class or need help with notes? Now, we've discussed numbers having square-roots in some {bf Q}_p (or {bf R} ) and not others.