Triple correlation of the Riemann zeros

We use the conjecture of Conrey, Farmer and Zirnbauer for averages of ratios of the Riemann zeta function to calculate all the lower order terms of the triple correlation function of the Riemann zeros. A previous approach was suggested in 1996 by Bogomolny and Keating taking inspiration from semi-classical methods. At that point they did not write out the answer explicitly, so we do that here, illustrating that by our method all the lower order terms down to the constant can be calculated rigourously if one assumes the ratios conjecture of Conrey, Farmer and Zirnbauer. Bogomolny and Keating returned to their previous results simultaneously with this current work, and have written out the full expression. The result presented in this paper agrees precisely with their formula, as well as with our numerical computations, which we include here. We also include an alternate proof of the triple correlation of eigenvalues from random U(N) matrices which follows a nearly identical method to that for the Riemann zeros, but is based on the theorem for averages of ratios of characteristic polynomials

Coupled Ocean Atmosphere Processes and European Climate (COAPEC): improved understanding of the coupled climate system

COAPEC (http://coapec.nerc.ac.uk/) is a five-year Directed Science Programme funded by the Natural Environment Research Council (NERC). COAPEC is providing advances in understanding the mechanisms by which the ocean and atmosphere interact, how these processes are represented in state-of-the-art numerical climate models and how they determine the predictability of the climate system over seasonal-decadal timescales. Processes studied include the generation and propagation of salinity and heat anomalies in the North Atlantic, the influence of the thermohaline circulation and the role of storm tracks on European Climate. The influence of remote processes, including ocean-atmosphere coupling in tropical Atlantic warm events and Southern Ocean circulation are also being investigated. As part of the programme, new coupled models are being developed, including: a coupled hybrid isopycnic coordinate model; fast models for multi-ensemble runs to investigate model parameters space, using both high performance machines and spare home PC resources; a QG model to investigate high resolution ocean processes in coupled systems and validated ice models for coupled modelling. Underpinning research into improving the observational datasets, such as the SOC flux climatology, and into the influence of sea-ice observations in General Circulation Models is also being carried out as part of the programme. To place these advances into a socially relevant context, COAPEC is also investigating the methods for using, and economic benefits of, climate forecasts at seasonal timescales for the UK health sector and the UK energy industry