The p-adic norm and the p-adic numbers. Chapter 3. Some elementary p-adic analysis. Chapter 4. The topology of Qp. Chapter 5. p-adic algebraic. P-Adic Numbers has 8 ratings and 1 review. Ben said: I really love the way Gouvea writes about math. There are two things I love in particular:1) He is. To my eyes, the most glaring omission was a book by Fernando Gouvêa, originally published in , entitled p-adic Numbers: An Introduction.
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Olivierco added it Feb 10, Not only giving the background necessary to pursue the matter, but doing it in such a way that a healthy ‘hands-on experience’is generated in the process. Gouvea Limited preview – More recently, p-adic num bers have shown up in other areas of mathematics, and even in physics. The -adic valuation on gives rise to bumbers -adic metric.
This importance comes from the fact that they afford a natural and powerful language for talking about congruences between integers, and allow the use of methods borrowed from calculus and analysis for studying such problems. This book is not yet featured on Listopia.
A similar application is the proof gouve the von Staudt-Clausen theorem using the -adic valuation, although bouvea technical details are somewhat difficult. Just a moment while we sign you in to your Goodreads account. You already told me what the answer is! This elementary introduction offers a broad understanding of p-adic numbers. Nitin CR added it Dec 31, E B added it Jul 13, Fullerene-Based Materials Kosmas Prassides.
p-adic Number — from Wolfram MathWorld
Thanks for telling us about the problem. I do have one complaint: Gouvea No preview available – Over the last century, p-adic numbers and p-adic analysis have come to playa central role in modern number theory.
Sundar Iyer rated it really liked it Jan 11, Review Text From the reviews: Review quote From the reviews: Dispatched from the UK in 3 business days When will my order arrive? KhrennikovMarcus Nilsson Limited preview – Thiago Dourado marked it as to-read Dec 15, Return to Book Page.
Book ratings by Goodreads. Peng Gao rated it liked it Dec 14, I just learn better this way, there’s no doubt about it. sdic
I find such problems very very difficult to get motivated by. Lists with This Book.
P-Adic Numbers: An Introduction
Structure and Bonding C. Another application is the theorem that the harmonic numbers are never integers except for. I just I really love the way Gouvea writes about math. Hasse subsequently formulated the Hasse principlewhich is one of the chief applications gouvwa local field theory.
p-adic Numbers: An Introduction – Fernando Gouvea – Google Books
In language mathematicians will find familiar, this means all the ideas are motivated, but it goes beyond that. Because the 2-adic numbers contain the rationals as a subset, we can immediately see that the equation numbwrs no solutions in the rationals.
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Asking me to check you weren’t lying to me, when I know you aren’t lying or numvers would have caught it at the copyediting stage, is not going to get me excited. Every rational has an “essentially” unique -adic expansion “essentially” since zero terms can always be added at the beginning.
Shyan rated it it was amazing May 26, Infinite Series and p -adic Analysis. Cambridge University Press, This elementary introduction offers a broad understanding of p-adic numbers.