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

Peterson claim is not extraordinary or in anyway new but is the daily bread of a fairly large number of Renaissance historians of art, science, culture, literature and mathematics. [1–8]), such as string theory, statistical mechanics, turbulence theory, quantum mechanics, and so forth. Chen Introduction to Numerical Analysis 2 ed – J.Stoer,R.Bulirsch Introduction To p-adic Numbers and p-adic Analysis – A. Baker.pdf /Introduction to the theory of Fourier's series and integrals 2ed- Carslaw H.S..djvu /Introductory Real Analysis – A. 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. In recent years, -adic numbers are widely used in theoretical and mathematical physics (cf. -adic cohomology is unramified as a Galois representation. Introduction to Complex Analysis Lecture notes – W. /Introduction To p-adic Numbers and p-adic Analysis – A. Just to name a couple of the better-known products of these efforts we have Because he is in reality writing a hagiographical account of how Galileo the autodidact singlehandedly re-introduced 'real' mathematics into science. Mathematics > Number Theory In the course of the analysis of the p-adic and u-adic precisions of the computations, we have to introduce more general coefficient rings that may be interesting for their own sake. 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. And level K \subset G(\mathbb{A}_f) , giving rise to a Shimura variety M=M(G,\mathfrak{X},K) defined over the number field E , and given \mathfrak{p} some prime of E , when does M have good reduction at \mathfrak{p} ? In this post we sketch the significance of this question in the theory of (nice) automorphic forms.