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

One fundamental construction in modern algebraic number theory is that of the completion of a number field with respect to an absolute value, the p-adic numbers being a particular case. *VFR He was an Islamic mathematician who wrote a large number of works including an introduction to Euclid's Elements, an algebra text and various works on astronomy. May18,2012, 14:30-17:30, B924 Zhixin Building, p-adic numbers and adeles. To do so, we need to introduced rational numbers, which are sort of ratios of two integer numbers… although this ratio is not uniquely defined by the choice of the two integers! Zhixin Building, A brief introduction to p-adics (1). 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? May17,2012, 14:30-17:30, B924 Zhixin Building, A brief introduction to p-adics (2). Very briefly, we can define an absolute value on \mathbf{Q} by defining it on \mathbf{Z} . Lecture notes on p-adic numbers by Andrew Baker Course notes for analytic number theory by Graham Everest; Distribution of Prime Numbers by William Chen; Introduction to Analytic Number Theory by Noam Elkies. Properties of numbers and letters. 1861 Kurt Hensel (29 Dec 1861 in Königsberg, Prussia (now Kaliningrad, Russia) - 1 June 1941 in Marburg, Germany) invented the p-adic numbers, an algebraic theory which has proved important in later applications. If you are not familiar with this, I don't know of a better gentle introduction than Fernando Gouvea's Introduction to the p -adic numbers.