title: RIEMANN ZEROS AND THE INVERSE PHASE PROBLEM.
abstract: Finding a universal method of crystal structure solution and proving the Riemann hypothesis are two outstanding challenges in apparently unrelated fields. For centrosymmetric crystals however, a connection arises as the result of a statistical approach to the inverse phase problem. It is shown that parameters of the phase distribution are related to the non-trivial Riemann zeros by a Mellin transform.
authors.affiliation: MRC Laboratory of Molecular Biology, Cambridge CB2 0QH, UK dst27@cam.ac.uk.
authors.forename: David S
authors.initials: DS
authors.lastname: Tourigny
keywords: Mellin transform; Riemann hypothesis; Riemann zeta function; X-ray diffraction; crystallography; maximum likelihood; structure factor