The research in the programme Number Theory ranges from algebraic number theory and group theory to analytic number theory and ergodic theory. A central theme is the design and application of algorithms in number theory. In algebraic number theory the focus is on algebraic units, class groups and Galois module structures. Methods from class field theory, homological algebra and analytic number theory play an important role. Methods from algebraic number theory and numerical mathematics are applied to factorization methods for large integers. Computational methods from algebraic number theory and Diophantine approximation are applied to determine all integer or even rational points on algebraic curves, and, besides ineffective methods, to study diophantine equations and recurrence sequences. Probabilistic and ergodic theoretical aspects of number expansions are investigated, in particular of -expansions and several different continued fraction expansions. This is interrelated with the study of Sturmian sequences. In group theory the research deals with representation theory of groups, Dade correspondence theory and extension theory of characters.

The coherence, size and intensity of the number theory research have been stimulated by the biweekly Number Theory Seminar. In the national `(groot) project' Number Theory De Weger, Moree and Hajdu were active at post-doc positions and Roskam as a graduate student. Furthermore, De Smit received a KNAW fellowship. The number theory programme acquired an enormous impetus through the Spinoza premium awarded to Lenstra. The award resulted in a professorship for Stevenhagen in Leiden. Furthermore it was possible to invite Schaefer as a visiting professor and various other scientists to Leiden during the spring semester of 1999. Moreover, some new Ph.D. students could be appointed.

In the spring of 1999 Granville occupied the Kloosterman Chair. In April 1999 the activities culminated in a workshop at the Lorentz Center.

In June 1999 Tijdeman received a honorary doctorate degree at the Kossuth Lajos University in Debrecen, Hungary.