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.