Introduction to P-Adic Numbers and Their Functions

a₁ algebraic integer an(y approximations assertion assume bounded called canonical Cassels Chapter choose coefficients components consider constant construction continuous function convergence defined definition denominator Denote derivative determine difference differentiable digits distinct divisible elements equal equation establish evidently example exists extension finally finitely follows formula function f(x fundamental sequence further g-adic number g-adic series g-adic value given giving Hence holds implies indefinitely infinite Lemma limit multiplication null sequence obtain orders p-adic field p-adic integer particular positive integer prime Problems Proof of Theorem prove pseudo-valuation rational integers rational numbers real numbers relative representation respectively result ring satisfy Similarly solution subsequence sufficient sufficient conditions theory unique valuation variable w(an whence write written zero zero divisor