Professor Martin Huxley
Emeritus Professor of Mathematics
- huxley@cardiff.ac.uk
- +44 (0)29 2087 5551
- E/1.10, 1st Floor, Mathematics Institute, Senghennydd Road, Cardiff, CF24 4AG
Overview
Research interests
Number Theory: prime numbers, the Riemann zeta function, Dirichlet polynomials, exponential sums, Dedekind sums, Kloosterman sums, the modular group, Maass wave forms, the Selberg and Kuznietsov trace formulae, lattice points in the plane, such as the Gauss circle problem, different configurations of lattice points inside a moving shape.
Spectral theory: The Laplacian on the upper half plane and hyperbolic orbifolds, eigenvalues and Eisenstein series.
Administrative duties
- Ethics Officer
- Library
Biography
Publications
2020
- Hill, S. L.et al. 2020. Some properties and applications of non-trivial divisor functions. Ramanujan Journal 51 (10.1007/s11139-018-0093-9)
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
- Huxley, M. N. 2018. A short account of the values of the zeta function at integers. Functiones et Approximatio Commentarii Mathematici 58(2), pp. 245-256. (10.7169/facm/1701)
2014
- Huxley, M. N. 2014. The tiled circle problem. Mathematika 60(2), pp. 321-346. (10.1112/S0025579313000211)
- Huxley, M. N. 2014. The convex hull of the lattice points inside a curve. Periodica Mathematica Hungarica 68(1), pp. 100-118. (10.1007/s10998-014-0024-5)
- Huxley, M. N. 2014. A fourth power discrepancy mean. Monatshefte für Mathematik 173(2), pp. 231-238. (10.1007/s00605-013-0558-2)
2013
- Huxley, M. N. and Zunic, J. 2013. The number of configurations in lattice point counting II. Proceedings of the London Mathematical Society 107(6), pp. 1331-1352. (10.1112/plms/pdt011)
- Huxley, M. N. 2013. Intersecting lines modulo one. Uniform Distribution Theory 8(2), pp. 1-28.
2012
- Huxley, M. N. 2012. Identities involving Farey fractions. Proceedings of the Steklov Institute of Mathematics 276(1), pp. 125-139. (10.1134/S0081543812010105)
- Huxley, M. N. 2012. Orthogonal functions with teeth. Chebyshevskii Sbornik
2011
- Huxley, M. N. 2011. A compactness lemma for convex plane sets. Eurasian Mathematical Journal 2(3), pp. 147-149.
2010
- Huxley, M. N. and Žunić, J. 2010. The number of configurations in lattice point counting I. Forum Mathematicum 22(1), pp. 127-152. (10.1515/FORUM.2010.007)
2009
- Huxley, M. N. and Konyagin, S. V. 2009. Cyclic polygons of integer points. Acta Arithmetica 138(2), pp. 109-136. (10.4064/aa138-2-2)
2007
- Huxley, M. N. and Žunić, J. 2007. The number of N point digital discs. IEEE Transactions on Pattern Analysis and Machine Intelligence 29(1), pp. 159-161.
- Huxley, M. N. and Ivic, A. 2007. Subconvexity for the Riemann zeta function and the divisor problem. Bulletin CXXXIV de l'Acad\'emie Serbe des Sciences et des Arts 32, pp. 13-32.
- Huxley, M. N. 2007. The integer points on a plane curve. Functiones et Approximatio, Commentarii Mathematici 37(1), pp. 213-231.
2006
- Huxley, M. N. and Zunic, J. 2006. Different digitizations of displaced discs. Foundations of computational mathematics 6(2), pp. 255-268. (10.1007/s10208-005-0177-y)
- Huxley, M. N. 2006. Is the Hlawka zeta function a respectable object?. Presented at: Symposia in Pure Mathematics 75Proc Symposia Pure Math 75. American Mathematical Society pp. 225-230.
- Huxley, M. N., Klette, R. and Zunic, J. 2006. Precision of geometric moments in picture analysis. In: Geometric Properties from Incomplete Data. Computational Imaging and Vision Vol. 31. Kluwer, pp. 221-235., (10.1007/1-4020-3858-8_12)
- Huxley, M. N. and Sargos, P. 2006. Points entiers au voisinage d'une courbe de classe C^n III. Functiones et Approximatio, Commentarii Mathematici 35(1), pp. 91-115.
2005
- Huxley, M. N. 2005. Exponential sums and the Riemann zeta function V. Proceedings of the London Mathematical Society 90(1), pp. 1-41. (10.1112/S0024611504014959)
- Huxley, M. N. 2005. The integer points close to a space curve. Presented at: Diophantine ApproximationsProceedings of Conference on Diophantine Approximations, Trudy Institit Matematiki (Minsk). Trudy Institit Matematiki (Minsk) pp. 94-113.
2004
- Huxley, M. N. 2004. Resonance curves in the Bombieri-Iwaniec method. Functiones et Approximatio Commentarii Mathematici 32, pp. 7-49.
- Huxley, M. N. and Zunic, J. 2004. On the number of digitisations of a disc depending on its position. In: Combinatorial Image Analysis. Lecture Notes in Computer Science Vol. 3322. Springer, pp. 219-231., (10.1007/978-3-540-30503-3_17)
- Huxley, M. N. 2004. The rational points close to a curve III. Acta Arithmetica 113, pp. 15-30. (10.4064/aa113-1-2)
2003
- Huxley, M. N. 2003. Exponential sums and lattice points III. Proceedings of the London Mathematical Society 87(3), pp. 591-609. (10.1112/S0024611503014485)
- Huxley, M. N. 2003. The rational points close to a curve IV. In: Bonner Mathematischen Schriften. Bonner Mathematischen Schriften Vol. 360. Bonn: Library of Mathematics
2001
- Huxley, M. N. and Watt, N. 2001. The number of ideals in a quadratic field II. Israel Journal of Mathematics 120(A), pp. 125-153.
Teaching
- MA0111 Elementary Number Theory I
- MA0212 Linear Algebra
- MA0216 Elementary Number Theory II
- MA0321 Coding Theory