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Mar 1, 2016 at 13:47 comment added Bertrand The Pólya-Vinogradov inequality provides an upper bound but does not provide any clue about what the maximum is doing below this bound for N increasing... I did not find any lower bound for this maximum that will increase for N increasing. So it seems (for me) a very hard problem to understand how this maximum behaves when N increases. I would like to show that an infinity of these maximum are lower than a fixed constant and I Wonder if this showing this is as hard as RH !
Feb 29, 2016 at 21:31 history edited GH from MO CC BY-SA 3.0
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Feb 29, 2016 at 21:23 history answered Fan Zheng CC BY-SA 3.0