# Chebyshev function: variational formulation

The Wikipedia article on the Chebyshev function $$\psi(x)$$ states that, evaluated at $$x=e^t$$, it minimizes the functional

$$J[f] = \int_0^\infty \dfrac{f(s)\zeta'(s+c)}{\zeta(s+c)(s+c)}ds - \int_0^\infty \int_0^\infty e^{-st}f(s)f(t)ds dt,$$

so that $$f(t) = \psi(e^t)e^{-ct}$$ for $$c>0$$.

Wikipedia lists no source for this. Can someone please point me to a text proving this (and possibly more on the connection between analytic number theory and variational calculus)?