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I'm not sure how suitable this question is, but I have had no response on Mathematics Stack Exchange. My original question is here: https://math.stackexchange.com/questions/3402938/uniformity-distributed-among-residue-classes

As a summary: On page 17 or Richert's Lectures on Sieves (http://www.math.utoledo.edu/~codenth/Spring_13/3200/NT-books/Lectures_on_Sieve_Methods-Richert.pdf),

It says equation 0.5 measures how uniformly the set $\gamma$ is distributed amongst the residue classes. But i don't understand how it does, or why the square is necessary.

Also, on page 18, I don't understand what is discussed in the paragraph labelled (A).

I have given my thoughts on these and attempted to think about it, detailed in the post on stackexchange.

Thanks.

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    $\begingroup$ D(p) is supposed to look like the variance between S(p,l) and its mean S/p; if it's relatively small it means that S(p,l) is very nearly S/p most of the time. That should get you thinking about what Richert is saying. Another nice property of D(p) is its positivity, which you need to apply things like Cauchy-Schwarz. $\endgroup$
    – Craig Franze
    Commented Nov 6, 2019 at 22:43
  • $\begingroup$ Thanks that makes sense! $\endgroup$
    – VBACODER
    Commented Nov 9, 2019 at 16:49

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