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

Moving on to an analogue over the p-adic numbers due to Tate. Ben: tell that to my referees in re the introductory sections to my papers. And completing yields the field of real numbers in the archimedean case, and the p -adic fields \mathbb{Q}_p for each prime p . These fields are useful in number theory for a variety of reasons, e.g., they have much simpler arithmetic structure ( Diophantine equations, and more generally, first order sentences are decidable, and the Galois groups of these fields are pro-solvable), and the . 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-adic Numbers: An IntroductionEbook Free Downloadp-adic Numbers: An Introduction. May17,2012, 14:30-17:30, B924 Zhixin Building, A brief introduction to p-adics (2). May18,2012, 14:30-17:30, B924 Zhixin Building, p-adic numbers and adeles. I've never been introduced to p-adic numbers before, but Professor Bhargava's simplified description made sense. It occured to me that I haven't defined a p -adic number on this blog yet. Zhixin Building, A brief introduction to p-adics (1).