On the harmonic continuation of the Riemann xi function

Abstract

We generalize the harmonic continuation of the Riemann xi-function to the $n$-dimension case, to obtain the solution to the Dirichlet problem on ${\mathbb{R}}_{+}^{n+1}.$ We also provide a new expansion for the harmonic continuation of the Riemann xi-function using an expansion given by R.J. Duffin.

Updated vector notation