= Selberg least-common-multiple weights
{c}
For real coefficients $\rho_1=1$ supported on permitted <divisors> up to $L$, put $\lambda_d=\sum_{[u,v]=d}\rho_u\rho_v$. Then $\sum_{d\mid n}\lambda_d=(\sum_{d\mid n}\rho_d)^2$ is an upper bound for the <indicator function> of numbers free of the forbidden <prime factors>. Its support has $d\leq L^2$. If the coefficients vanish on non-<squarefree integers> and satisfy $|\rho_d|\leq1$, then $|\lambda_d|\leq3^{\omega(d)}$: each <prime factor> of $d$ occurs in $u$, in $v$, or in both.
Back to article page
