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Mar 6, 2016 at 19:42 comment added Bertrand @Koukoulopoulos the only lower bound I found for this sequence of $Max$ is a constant (because the character are induced). For primitive character the $Max$ of partial sum increases with modulus (and lower bound depending on modulus exists) but for induced characters, what can we say ?
Mar 6, 2016 at 19:26 comment added Bertrand Dear Dimitris thanks for your help, you have shown that the upper bound can be improved, but is there an increasing lower bound ? I am intereseted to find in this sequence of character an infinite number having their $Max|(S(x,y)|$ lower than a fixed constant, do you think it is possible or realistic ? or the $Max$ is converging to infinity ?
Mar 3, 2016 at 23:09 history edited Dimitris Koukoulopoulos CC BY-SA 3.0
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Mar 3, 2016 at 22:19 history answered Dimitris Koukoulopoulos CC BY-SA 3.0