In 1997, the author proved that the Riemann hypothesis holds if and only
if $\lambda_n=\sum [1-(1-1/\rho)^n]>0$ for all positive integers $n$,
where the sum is over all complex zeros of the Riemann zeta function.
In 1999, E. Bombieri and J. Lagarias generalized this result and
obtained a remarkable general theorem about the location of zeros. They
also gave an arithmetic interpretation for the numbers $\lambda_n$. In
this note, the author extends Bombieri and Lagarias' arithmetic formula
to Dirichlet $L$-functions and to $L$-series of elliptic curves over
rational numbers.