engleski

Quadratic approximation in Q_p

Let p be a prime number. Let w_2 and w_2^* denote the exponents of approximation defined by Mahler and Koksma, respectively, in their classifications of p-adic numbers. It is well-known that every p- adic number x satisfies w_2^*(x) <=w_2(x)<=w_2^* (x)+1, with w_2^* (x)=w_2(x)=2 for almost all x. By means of Schneider's continued fractions, we give explicit examples of p-adic numbers x for which the function w_2-w_2^* takes any prescribed value in the interval (0, 1].

p-adic Diophantine approximation ; Mahler's classification ; Koksma's classification ; quadratic approximation

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