p-adic numbers: An introduction Fernando Quadros Gouvea
Publisher: Springer

Introduction to p-adic integers. I feel like taking a break from elliptic curves and talking about something completely different. It seems to me p-adic numbers and p-adic analysis always provide with good examples. It might be worth trying out for some values of p! , we will probably get a different value than if we had evaluated it in the real numbers. The usual construction of p-adic numbers is pretty complicated for the nonexpert. P-adic Variation in Number Theory (in honor of Glenn Stevens 60th birthday), June 2-6, 2014, Boston University Lattice Basis Reduction: An Introduction to the LLL Algorithm and Its Applications, Murray R. Introduction to path integrals in field theory (Skriptum Uni-Giessen 1999). A book written by Neal Koblitz (GTM 58) seems to be a good introduction to this field. Keywords » Tate's thesis – automorphic L-functions – modular forms – tensor product theorem. For motivation, let's take a look at solutions of the equation x^2 + x + 3 quiv 0 pmod{5^r for different values of by f(x) and 5 by p. The set of rational numbers is the set of numbers that can be written as a fraction. LINK: Download Introduction to p-adic numbers and valuation theory Audiobook. Introduction to p-adic numbers and valuation theory. As a profound application of model theory in algebra, the last part of this book develops a complete proof of Ax and Kochen's work on Artin's conjecture about Diophantine properties of p-adic number fields. But, here's the idea in a nutshell. Introduction To p-adic Numbers and p-adic Analysis A. I will read the first chapter of it (only twenty pages). We know that there exists a solution a_r bmod p^r to equation f(a_r) quiv 0 pmod{p^r}. There are many books on Automorphic forms but this is the first book that requires only few pre-requisites and definitely is suitable for advanced undergraduate There a lot of books and material for p-Adic numbers and the author just spend 15 pages discussing this topic. Examples of rational numbers are 4, 13, 2.1, 22/7, 0.333333… . Futher, we will always assume that p is prime. This book is an elementary introduction to the realm of Automorphic forms. Dave Richeson of 'Divison by Zero' knows what they are though and gave a basic introduction to them back in November.