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Let's consider the Dirichlet Character $\chi_3(n)$ modulo 3 given by $\chi_3(1)=1$, $\chi_3(2)=-1$ and $\chi_3(3)=\chi_3(0)=0$. Lets consider the sequence of induced characters $\chi^{P_N} $ obtained ...

Consider a Dirichlet character, $\chi(n)$, and the partial sum : $$S(\chi,x)=\bigg |\sum_{n=1}^{x} \chi(n)\bigg|$$ There are many works to bound this sum when $\chi$ is a primitive character, but ...