Abstract. We have given some arguments that a two-dimensional Lorentz-invariant Hamiltonian may be relevant to the Riemann hypothesis concerning zero points of the Riemann zeta function. Some eigenfunction of the Hamiltonian corresponding to infinite-dimensional representation of the Lorentz group have many interesting properties. Especially, a relationship exists between the zero zeta-function condition and the absence of trivial representations in the wavefunction. We also give a heuristic argument for the validity of the hypothesis.

Print publication: Issue 3 (23 January 1998)
Received 22 July 1997, in final form 15 September 1997