I have a functionfholomorphic on D(0;R).

s, rsuch that (r < s < R)

M(r)= sup { |f(z)| : z = r } (r < R)

M(s)= sup { |f(z)| : z = s } (s < R)

I was asked to show thatM(r) <= M(s)and I have used the Maximum Modulus and the Identity theorems to accomplish that.

The next part of question asks to show thatM(r) r^(-n) >= M(s) s^(-n)whenfis a polynomial of degree n 0 < r < s < R.

I know that f(z) = Sum ( Cn (z - a)^n ) from 0 to inf

and

M(r) r^(-n) >= | An |

M(s) r^(-n) >= | Bn |

Could someone push me in the right direction?

Thanks!