  We study an arithmetic analog of the Hall algebra of a curve, when the curve
is replaced by the spectrum of the integers compactified at infinity. The role
of vector bundles is played by lattices with quadratic forms. This algebra H
consists of automorphic forms with respect to GL_n(Z), n>0, with multiplication
given by the parabolic pseudo-Eisenstein series map.
  We concentrate on the subalgebra SH in H generated by functions on the
Arakelov Picard group of Spec(Z). We identify H with a Feigin-Odesskii type
shuffle algebra, with the function defining the shuffle algebra expressed
through the Riemann zeta function. As an application we study relations in H.
Quadratic relations express the functional equation for the Eisenstein-Maass
series. We show that the space of additional cubic relations (lying an an
appropriate completion of H and considered modulo rescaling), is identified
with the space spanned by nontrivial zeroes of the zeta function.
