Dr Matthew Lettington
Lecturer
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Following the award of my PhD (Number Theory) in 2010, I joined Cardiff University as a Lecturer, obtaining a tenured position as an SBP Fellow in May 2012.
Administrative duties
Undergraduate Project Co-Ordinator
School of Mathematics Newsletter Editor
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2021
- Higham, N. J., Lettington, M. C. and Schmidt, K. M. 2021. Integer matrix factorisations, superalgebras and the quadratic form obstruction. Linear Algebra and its Applications 622, pp. 250-267. (10.1016/j.laa.2021.03.028)
- Higham, N. J. and Lettington, M. C. 2021. Optimizing and factorizing the Wilson Matrix. American Mathematical Monthly
2020
- Lettington, M. C. and Schmidt, K. M. 2020. Divisor functions and the number of sum systems. Integers 20, article number: A61.
- Hill, S. L.et al. 2020. Some properties and applications of non-trivial divisor functions. Ramanujan Journal 51 (10.1007/s11139-018-0093-9)
- Coffey, M. W. and Lettington, M. C. 2020. Binomial polynomials mimicking Riemann's zeta function. Integral Transforms and Special Functions 31(11), pp. 856-872. (10.1080/10652469.2020.1755672)
2019
- Huxley, M. N., Lettington, M. C. and Schmidt, K. M. 2019. On the structure of additive systems of integers. Periodica Mathematica Hungarica 78, pp. 178-199. (10.1007/s10998-018-00275-w)
2018
- Hill, S., Lettington, M. C. and Schmidt, K. M. 2018. Block representations and spectral properties of constant sum matrices. Electronic Journal of Linear Algebra 34, pp. 170-190. (10.13001/1081-3810.3530)
2017
- Lettington, M. C., Schmidt, K. M. and Hill, S. 2017. On superalgebras of matrices with symmetry properties. Linear and Multilinear Algebra 66(8), pp. 1538-1563. (10.1080/03081087.2017.1363153)
- Coffey, M. W.et al. 2017. On higher-dimensional Fibonacci numbers, Chebyshev polynomials and sequences of vector convergents. Journal de Theorie des Nombres de Bordeaux 29(2), pp. 369-423. (10.5802/jtnb.985)
- Coffey, M. W. and Lettington, M. C. 2017. Binomial polynomials mimicking Riemann's Zeta Function. arXiv, article number: arXiv:1703.09251.
2016
- Lettington, M. and Coffey, M. W. 2016. On fibonacci polynomial expressions for sums of m-th powers, their implications for faulhaber's formula and some theorems of fermat. arXiv, article number: 1510.05402.
2015
- Coffey, M. W. and Lettington, M. C. 2015. Mellin transforms with only critical zeros: Legendre functions. Journal of Number Theory 148, pp. 507-536. (10.1016/j.jnt.2014.07.021)
2014
- Brunnock, R., Lettington, M. C. and Schmidt, K. M. 2014. On square roots and norms of matrices with symmetry properties. Linear Algebra and its Applications 459, pp. 175-207. (10.1016/j.laa.2014.06.054)
2013
- Lettington, M. C. 2013. A trio of Bernoulli relations, their implications for the Ramanujan polynomials and the special values of the Riemann zeta function. Acta Arithmetica 158(1), pp. 1-31. (10.4064/aa158-1-1)
2011
- Lettington, M. C. 2011. Fleck's congruence, associated magic squares and a zeta identity. Functiones et Approximatio, Commentarii Mathematici 45(2), pp. 165-205. (10.7169/facm/1323705813)
2010
- Lettington, M. C. 2010. Integer points close to convex hypersurfaces. Acta Arithmetica 141(1), pp. 73-101. (10.4064/aa141-1-4)
2009
- Lettington, M. C. 2009. Integer points close to convex surfaces. Acta Arithmetica 138(1), pp. 1-23. (10.4064/aa138-1-1)
2008
- Lettington, M. C. 2008. Topics related to the theory of numbers: integer points close to convex hypersurfaces, associated magic squares and a zeta identity. PhD Thesis, Cardiff University.
Addysgu
- MA4011 Analytic Number Theory
- MA0216 Elementary Number Theory II
- MA3004 Combinatorics
Research interests:
- Integer points close to convex hypersurfaces and polytopes.
- Identities for the Zeta function at integer values.
- Combinatorial and number theoretic properties of symmetric matrices under matrix multiplication.
- Modelling techniques for industry (such as SSA).
Supervision
Project Descriptions
The general theme is centred on constructions and limits of sequences of vector convergents, systems of polynomials and generating function matrices, including the application of special function theory. There are a number of possible directions within this project as there are currently many areas that are of interest from description/categorisation theories to general unifying approaches and extensions of current methodologies
The student will learn about ideas from number theory and mathematical analysis. The project will involve an element of numerical analysis via Mathematica.
The student will learn about ideas from number theory and mathematical analysis. The project will involve an element of numerical analysis via Mathematica.
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Past projects
Successful previous PhD students:
- Dilbak Mohammed (second supervisor)