Skip to content
Skip to navigation menu

Dr Nigel Watt

Overview

Position: Lecturer in Mathematics Email: wattn@cardiff.ac.uk
Telephone: +44(0)29 298 75670
Fax: +44(0)29 208 74199
Extension: 75670
Location: M/2.44

Research Interests

Bounds for Weyl type exponential sums: applications to the Riemann zeta-function, the circle problem, the divisor problem, and allied topics. Sums involving Fourier coefficients of modular forms and mean-value theorems for L-functions: applications concerning the distribution of prime numbers in short intervals and in arithmetic progressions, and applications concerning the distributions of Gaussian primes in the complex plane.

Research Group

Number Theory

Recent Publications

Watt N, Fourier coefficients of modular forms and eigenvalues of a Hecke operator,  Functiones et Approximatio Commentarii Methematici, 2005, 27-146, 34.

Watt N, Harman G and Wong K, A new mean-value result for Dirichlet L-functions and polynomials, The Quarterly Journal of Mathematics, 2004, 307-324, 55 (3).

Watt N, On the mean-squared modulus of a Dirichlet L-function over a short segment of the critical line, Acta Arithmetica, 2004, 307-403, 111 (4).

Watt N, On differences of semicubical powers, Monatshefte für Mathematik, 2004, 45-81, 141 (1).

Teaching

MA0202 Methods of Matrix Algebra

MA0111 Elementary Number Theory I

MA0216 Elementary Number Theory II

Supervision of a Final Year Student Project (Partitions and Generating Functions)

Administrative Duties

Secretary of the Final Year Examination Board, Personal Tutor, UCAS interviewer

Publications

MathSciNet

Search MathSciNet

Please be aware that MathSciNet searching is only possible if you are accessing this page from an institution with a MathSciNet subscription.

Google Scholar

Search Google Scholar

1. M. N. Huxley and N. Watt, ‘Exponential sums and the Riemann zeta function’, Proc. London Math. Soc. 57 (1988) 1-24.

2. N. Watt, ‘A problem on semicubical powers’, Acta Arith. 52 (1988) 119-140.

3. M. N. Huxley and N. Watt, ‘The Hardy-Littlewood Method for exponential sums’, Colloq. Math. Soc. Janos Bolyai 51 (1987) 173-191

4. N. Watt, ‘Exponential sums and the Riemann zeta-function II’, J. London Math. Soc. (2) 39 (1989) 385-404

5. M. N. Huxley and N.Watt, ‘Exponential sums with a parameter’, Proc. London Math. Soc. (3) 59 (1989) 233-252

6. N. Watt, ‘An elementary treatment of a general Diophantine problem’, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 15 (1988) 603-614

7. N. Watt, ‘A problem on square-roots of integers’, Periodica Mathematica Hungarica 21 (1) (1990) 55-64

8. N. Watt, ‘A hybrid bound for Dirichlet L-functions on the critical line’, Proceedings of the Amalfi Conference on Analytic Number Theory (University of Salerno 1992), 387-392.

9. N. Watt, ‘Kloosterman sums and a mean value for Dirichlet polynomials’, J. Number Theory (1) 53 (1995), 179-210.

10. M. N. Huxley and N. Watt, ‘The number of ideals in a quadratic field’, Proc. Indian Acad. Sci. (Math. Sci.), Vol. 104, No. 1, February 1994, pp. 157-165.

11. N. Watt, ‘Short intervals almost all containing primes’, Acta Arith. (2) 72 (1995), 131-167.

12. J. Br¨udern and N. Watt, ‘On Waring’s Problem for four cubes’, Duke Math. J. (3) 77 (1995), 583-606.

13. M. N. Huxley and N. Watt, ‘Congruence families of exponential sums’, Proceedings of the 39th Taniguchi International Symposium on Mathematics (Analytic Number Theory), Kyoto, 1996, London Math. Soc. Lecture Note Series 247 (C.U.P. 1997), 127-138.

14. N. Watt, ‘On similar short sums’, Mathematika 46 (1999), 193-204.

15. M. N. Huxley and N. Watt, ‘The number of ideals in a quadratic field, II’, Israel J. Math. 120 (2000), part A, 125-153.

16. M. N. Huxley and N. Watt, ‘Hybrid bounds for Dirichlet’s L-function’, Math. Proc. Cam. Phil. Soc. 129 (2000), 385-415.

17. Watt N, On differences of semicubical powers, Monatshefte für Mathematik, 2004, 45-81, 141 (1).

18. Watt N, On the mean-squared modulus of a Dirichlet L-function over a short segment of the critical line, Acta Arithmetica, 2004, 307-403, 111 (4).

19. Watt N, Harman G and Wong K, A new mean-value result for Dirichlet L -functions and polynomials, The Quarterly Journal of Mathematics, 2004, 307-324, 55 (3).

20. Watt N, Fourier coefficients of modular forms and eigenvalues of a Hecke operator, Functiones et Approximatio, Commentarii Mathematici, 2005, 27-146, 34.

21. Watt N, Bounds for a Mean Value of Character Sums, to appear in the International Journal of Number Theory.

Research

External Funding Since 2000

10/2004-9/2006: Research Fellowship associated with the EPSRC funded project `The Development and Application of Mean-Value Results in Multiplicative Number Theory’ (GR/T20236/01) [Principal Researcher: Prof. Glyn Harman of Royal Holloway, University of London]

Major Conference Talks Since 2004

September 2004, at the Workshop on `Theory of the Riemann Zeta and Allied Functions’ in Oberwolfach. Title: `Analogues for results of Deshouillers and Iwaniec’

December 2005, at the conference on `Applications of Representation Theory to Analytic Number Theory’ in Haifa. Title: `Character sums and eigenvalues of a Hecke operator’

July 2007, at the 25th `Journees Arithmetiques’ in Edinburgh: Title: `A mean-value of Hecke L-functions’

Biography

BSc in Mathematics – St Andrews University, 1984

Certificate of Advanced Study in Mathematics - Cambridge University, 1985

PhD – University of Wales (University College, Cardiff), 1988. Thesis title: `Some topics in Analytic Number Theory’

MSc in Machine Perception and Neurocomputing – Keele University, 1999

Previous Positions

Since 1989 I have held a sequence of full-time positions at the following institutions: Rutgers University (New Jersey, USA), University of Wales (College of Cardiff) in the UK,

University of Goettingen (Germany), University of Nottingham (UK), Hail Community College (Kingdom of Saudi Arabia), U.G.R.U. in Al Ain University (United Arab Emirates), Royal Holloway, University of London (UK). I have also worked Part-Time at the University of Edinburgh.