Details of Grant 

EPSRC Reference:	GR/T00641/01
Title:	Values of L-functions & Random Matrix Theory
Principal Investigator:	Keating, Professor J
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	Mathematics
Organisation:	University of Bristol
Scheme:	Senior Fellowship (Pre-FEC)
Starts:	01 October 2004	Ends:	30 September 2009	Value (£):	353,916
EPSRC Research Topic Classifications:	Algebra & Geometry Mathematical Physics
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:	Panel Date Panel Name Outcome 26 May 2004 Fellowships Central Allocation Panel Deferred 12 Mar 2004 Maths Fellowships Sifting Panel 2004 Deferred
Summary on Grant Application Form
The Riemann zeta function encodes information about the prime numbers, the building-blocks of arithmetic. It is the subject of Riemann Hypothesis, which has been recognized for over 100 years as perhaps the most important unsolved problem in mathematics. Recently, evidence has emerged of fundamental links between properties of the Riemann zeta function and those of complex quantum systems: it appears that techniques developed to describe complex quantum systems, such as atomic nuclei and microelectronic devices, also describe some very important features of the zeta function. These techniques go under the general name of Random Matrix Theory. Their relationship with the zeta function is still mysterious, but it hints at profound connections between pure mathematics and mathematical physics. The aim of the research programme is to explore this relationship further and, in particular, to investigate whether it can be extended to cast new light on some other very important and long-standing problems in number theory. These problems can all be expressed in terms of functions, called L-functions, that are very closely related to the Riemann zeta function. The main idea will be to use random matrix theory to predict the probability that these L-functions take particular values. This research will cross traditional boundaries in that it will involve combining methods and ideas from pure mathematics and mathematical physics. Collaborations with researchers from both areas will be central to its success.
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Organisation Website:	http://www.bris.ac.uk