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Sep 9, 2014 at 11:43 vote accept mohi
May 23, 2014 at 17:19 answer added mohi timeline score: 2
May 22, 2014 at 18:05 comment added mohi Thanks! I forgot to mention the relationship between m and n. I have added this in the above
May 22, 2014 at 18:05 history edited mohi CC BY-SA 3.0
added 213 characters in body
May 22, 2014 at 17:57 comment added fedja Whether your hope is true or not, certainly depends on the relation between $m$ and $n$. Let's take two extremes: 1) $m=1$. Then the discrepancy factor is like $n^2$. 2) $m=\infty$. Then the law of large numbers tells you that your quantity is essentially the same for all $x$.
May 22, 2014 at 17:16 history asked mohi CC BY-SA 3.0