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Nov 29, 2014 at 5:59 history edited Kirill CC BY-SA 3.0
Changed the definition of the sum as pointed out in the answer.
Nov 29, 2014 at 4:54 vote accept Kirill
Nov 28, 2014 at 5:54 answer added Denis Chaperon de Lauzières timeline score: 6
Nov 28, 2014 at 5:18 history edited Kirill CC BY-SA 3.0
added 137 characters in body
Nov 28, 2014 at 0:28 history edited Kirill CC BY-SA 3.0
added 137 characters in body
Nov 28, 2014 at 0:25 comment added Noam D. Elkies It's certainly $O(p^{1/2 + o(1)})$ by the usual trick of writing the characteristic function of $[0,m]$ as a linear combination of complex exponentials. I suspect the imaginary part of a partial sum is not quite $O(p^{1/2})$ as you hope.
Nov 28, 2014 at 0:19 history asked Kirill CC BY-SA 3.0