Exam question - correlation function

Sojourner01
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Homework Statement



This is a question from an exam in fractals and chaos. The paper is attached, the question is the first one, part (b).

Homework Equations



In the paper

The Attempt at a Solution



Am I expected to compute continuous correlation functions with respect to epsilon for each point? This sounds like an obscene amount of work for the time given. Or am I misunderstanding what is being asked for?
 

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Nobody? This might come up in my exam tomorrow so I'm pretty anxious to know...
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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