A problem about primitive Dirichlet characters - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T00:52:37Z http://mathoverflow.net/feeds/question/110860 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/110860/a-problem-about-primitive-dirichlet-characters A problem about primitive Dirichlet characters nam 2012-10-27T21:38:18Z 2012-10-28T01:05:38Z <p>Show that for a primitive character $\chi\bmod q$, $q\gt1$ </p> <p>$\sum_{|n|\le q}(1-|n|/q)\chi(n)e(na)\ll\sqrt q$ uniformly in $a$, where $e(na)=\exp(2\pi ina)$</p> <p>Thank you for any comment.</p>