p-adic Numbers: An IntroductionSpringer Science & Business Media, 29.06.2013 - 282 Seiten p-adic numbers are of great theoretical importance in number theory, since they allow the use of the language of analysis to study problems relating toprime numbers and diophantine equations. Further, they offer a realm where one can do things that are very similar to classical analysis, but with results that are quite unusual. The book should be of use to students interested in number theory, but at the same time offers an interesting example of the many connections between different parts of mathematics. The book strives to be understandable to an undergraduate audience. Very little background has been assumed, and the presentation is leisurely. There are many problems, which should help readers who are working on their own (a large appendix with hints on the problem is included). Most of all, the book should offer undergraduates exposure to some interesting mathematics which is off the beaten track. Those who will later specialize in number theory, algebraic geometry, and related subjects will benefit more directly, but all mathematics students can enjoy the book. |
Inhalt
1 | |
padic Numbers | 16 |
Elementary Analysis in | 84 |
Vector Spaces and Field Extensions | 117 |
Analysis in Cp | 171 |
A Hints and Comments on the Problems 221 | 222 |
BA Brief Glance at the Literature | 273 |
279 | |
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
a₁ a₁X algebraic closure analysis archimedian ball of radius Cauchy sequence closed ball closed unit ball coefficients complete with respect compute condition congruent consider contains Corollary defined definition divisible easy element equal equation example exists extension of Qp fact factors finite extension follows function gives h₁(X hence Hensel's Lemma Hint inequality infinite irreducible polynomial isomorphism Let f(X metric modulo monic Newton polygon non-archimedian absolute value norm Notice number theory open ball p-adic absolute value p-adic analysis p-adic expansion p-adic numbers positive real number power series prime Problem proof properties Proposition prove quotient rational numbers reader region of convergence residue field ring roots of unity satisfies says slope solution Suppose tends to zero topology U₁ unramified vector space vp(x Weierstrass Preparation Theorem Zp[X