engleski

Schneider's p-adic continued fractions

We study Schneider's version of p-adic continued fractions. We are interested in the finiteness of rational number expansion, the quality of approximation by convergents, the irrationality exponent of a number with a given continued fraction expansion, and the convergence of Schneider's continued fractions in the field of real numbers. The main requirement for all of these problems is a good estimate of growth for the sequences of numerators and denominators of convergents. These sequences satisfy second order linear recurrence relations with nonconstant coefficients.

p-adic numbers ; continued fractions ; irrationality exponent

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