I was wondering if someone could explain how pade approximants are used to find good diophnatine approximations to algebraic numbers but in simple terms, for someone that's not an expert in this field.
In particular I was looking at pade approximants to z^(1/n) about say z=1, what would these look like? Are the coefficients rational number and if so why?
Also what's special about pade approximants that they give such dense rational approixmations to rational numbers (a/b)^(1/n) ? e.g. cubed root of 2. Just how good are these approximations (I know they can often be used to prove the irrationality of the number)
Are there any main theorems that would help in working/understanding pade approximants?