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

Recently there was an intriguing breakthrough in the study of partition numbers. I feel like taking a break from elliptic curves and talking about something completely different. Publisher: Academic Press Page Count: 182. Author: George Bachman Type: eBook. At last I found a very good introduction to the subject of p-adic numbers in a physics report article about p-adic strings so I didn´t go too far with topological geometrodynamics. Http: //en.wikipedia.org/wiki/P-adic_Hodge_theory The general strategy of p-adic Hodge theory, introduced by Fontaine, is to construct certain so-called period rings. Futher, we will always assume that p is prime. Language: English Released: 1964. GO Introduction to p-adic numbers and valuation theory. Partitions numbers P(n) count the number of ways of expressing n as a sum of positive integers. We know that there exists a solution a_r \bmod p^r to equation f(a_r) \equiv 0 \pmod{p^r}. P(4) = 5 because 4 = 1+1+1+1 = 1+1+2 = 1+3 = 2+2 = 4. Introduction to p-adic integers. For motivation, let's take a look at solutions of the equation x^2 + x + 3 \equiv 0 \pmod{5^r for different values of by f(x) and 5 by p.