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

You can read about this in the book 'A course in arithmetic' by J.-P. I mentioned in lecture something called the Hasse Principle, which holds for simple kinds of equations. May18,2012, 14:30-17:30, B924 Zhixin Building, p-adic numbers and adeles. May17,2012, 14:30-17:30, B924 Zhixin Building, A brief introduction to p-adics (2). Here's what we've done so far : 1st lecture was all about ideles and adeles (of Q) strarting with introducing p-adic numbers and ending with all the topological facts about idele-classes, the diagonal embedding of Q being discrete and that stuff. , we will probably get a different value than if we had evaluated it in the real numbers. Now, we've discussed numbers having square-roots in some {\bf Q}_p (or {\bf R} ) and not others. 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. Zhixin Building, A brief introduction to p-adics (1). I highly recommend this book as an introduction to the theory of Diophantine equations with a different flavor from the present course. It might be worth trying out for some values of p! P-adic Numbers: An IntroductionEbook Free Downloadp-adic Numbers: An Introduction. P-adic Numbers, p-adic Analysis, and Zeta-Functions (Graduate Texts in Mathematics) (v.