Nonnegative zeta-times-real-L coefficients
= Nonnegative zeta-times-real-L coefficients
{title2=$a_n=\sum_{d\mid n}\chi(d)\ge0\quad(\chi\text{ real})$}
The coefficients of $\zeta(s)L(s,\chi)$ are multiplicative. On $p^k$, their values are $k+1$ when $\chi(p)=1$, alternating one and zero when $\chi(p)=-1$, and one when $\chi(p)=0$. In particular $a_{m^2}\ge1$. Their logarithmic Euler coefficients $\Lambda(n)(1+\chi(n))$ are also nonnegative, supporting <uniqueness of a possible exceptional real Dirichlet zero>.