| EPSRC Reference: |
GR/T00658/01 |
| Title: |
Values of L-functions & Random Matrix Theory |
| Principal Investigator: |
Keating, Professor J |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Mathematics |
| Organisation: |
University of Bristol |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
06 June 2005 |
Ends: |
05 June 2008 |
Value (£): |
151,100
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| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Mathematical Physics |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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| Related Grants: |
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| Panel History: |
| Panel Date | Panel Name | Outcome |
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26 May 2004
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Fellowships Central Allocation Panel
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Deferred
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Summary on Grant Application Form |
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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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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.bris.ac.uk |