| EPSRC Reference: |
EP/I018824/1 |
| Title: |
Forms in many variables |
| Principal Investigator: |
Dietmann, Dr R |
| Other Investigators: |
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| Department: |
Mathematics |
| Organisation: |
Royal Holloway, Univ of London |
| Scheme: |
First Grant - Revised 2009 |
| Starts: |
03 May 2011 |
Ends: |
02 November 2012 |
Value (£): |
101,624
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| EPSRC Research Topic Classifications: |
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| 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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24 Nov 2010
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Mathematics Responsive Mode Prioritisation Panel
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Announced
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Summary on Grant Application Form |
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A Diophantine equation is an equation to be solved in integers (the sequence 1,2,3,... are the positive integers), for example(*) x^2+y^2=z^2has the integer solution (x,y,z)=(3,4,5). This example is a so called quadratic equation ,since all terms occur as a square. One can also consider Diophantine inequalities, for which oneis interested in making a certain quantity, for example a x^2 + b y^2 + c z^2 very small , where now a,b,c are real numbers like 3.141..., but x,y,y are still integers.The proposed research deals with an important subclass of Diophantine equations/Diophantine inequalitiesand aims to advance our knowledge in several key aspects, in particular:1) Since dealing with individual Diophantine problems is extremely hard, we aim to do better on average .2) Our second goal is to study quantitative aspects like the number of solutions for quadratic Diophantine equations.3) We want to discuss not only solutions of Diophantine equations in integers, but also in primes numbers(a prime number is an integer exceeding 1 and only divisible by 1 and itself, like 2,3,5,...)This research addresses key aspects of pure mathematics, in particular number theory, and its main benefitsand applications are are again in pure mathematics, in particular number theory.
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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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