My main research is in number theory, that is, the study of the properties of the whole numbers, especially by the use of analytic techniques. Particular subjects of interest are Waring's problem, the Goldbach problem, the Hardy-Littlewood method, the use of "smooth numbers", i.e. numbers without large prime factors, the distribution of prime numbers, exponential sums over integer sequences such as the sequence of primes, properties of the Riemann zeta-function and Dirichlet L-functions and diophantine approximation.