The conformal Laplacian of the Riemann xi-function has spectrum [0, ∞)

The Friedrichs Laplacian associated with the conformal metric |F(s)|² |ds|² has spectrum [0, ∞) whenever F is holomorphic and zero-free for Re(s) ≥ 2, is positive on the real axis, tends to infinity along the positive real axis, and has a logarithmic derivative F′/F that grows at most logarithmically in the strip |Im(s)| ≤ 1. The Riemann xi-function satisfies these assumptions. Consequently, the corresponding operator is not a Hilbert–Pólya operator. This note makes no claim about the Riemann hypothesis. A Portuguese version is included.