Something between the conjectures of Pólya and Turán implies the Riemann hypothesis

Abstract:

One could prove the Riemann hypothesis if one could show that some certain arithmetical sums are of a constant sign. Two such sums, studied by Pólya and Turán, are known not to be of a constant sign. Mike Mossinghoff and I looked at generalisations of these sums; in this talk, I will give details of the sum most likely to be of constant sign.