Explicit formula for the discrete Laplace transform of the Möbius function, related special functions, and a criterion for the Riemann hypothesis

In this paper, we assume that all the zeros of the Riemann zeta function are simple. Under this assumption we give an explicit formula for the function $Φ(e^{-t})=\sum_{n=1}^{\infty}μ(n)e^{-nt}$, as a function of the values of $ζ(s)$ and $ζ'(s)$ at the odd integers and as a function of the zeros of