# Something between the conjectures of P\'{o}lya and Tur\'{a}n implies the Riemann hypothesis.

*Algebra/Geometry/Topology Seminar*

*by Timothy Trudgian*

*Institution:*Australian National University

*Date: Wed 21st November 2012*

*Time: 11:00 AM*

*Location: 213 Richard Berry*

*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 P\'{o}lya and Tur\'{a}n, 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.