# Number theory

The research group in number theory exists since 1990. It has grown considerably since then:

• Robert Tichy (Discrepancy theory, Diophantine equations, analytic and algorithmic number theory, Quasi-Monte Carlo methods and applications in mathematical finance)
• Peter Grabner (Uniform distribution and arithmetic dynamical systems, asymptotic analysis, analytic combinatorics, Fractal Structures in Number Theory)
• Christian Elsholtz (combinatorial and additive number theory, analytic number theory, prime numbers, diophantine equations)
• Christoph Aistleitner (probabilistic methods in analysis and number theory, analytic number theory, limit laws in probability)
• Dijana Kreso (diophantine equations, polynomials)
• Kostadinka Lapkova (analytic number theory, class numbers, divisor estimates)
• Marc Munsch (analytic number theory, L-functions, theta functions, modular forms, character sums)
• Stefan Planitzer (analytic number theory)
• Marc Technau (analytic number theory, primes)
• Mario Weitzer (arithmetic dynamical systems, discrete geometry)
• Agamemnon Zafeiropoulos

and several further PhD students.

Former members:

Christopher Frei (analytic number theory and algebraic geometry, lattice points on varieties)

Antoine Marnat (geometric number theory, Diophantine approximation)

Former members of the group also include: Clemens Fuchs (Salzburg), Clemens Heuberger (Klagenfurt), Manfred Madritsch (Nancy), Bruno Martin (Calais) Thomas Stoll (Nancy), Martin Widmer (Royal Holloway, London).

We have regular contacts with colleagues in Debrecen, Zagreb, Budapest, Royal Holloway, Marseille, Nancy, Paris, Beersheba, Rostock, UNSW and Macquarie University, and many other places.

Our seminars are announced in the general TU Graz maths seminar list (fosp).

There are further seminars in algebra and number theory at Karl Franzens University Graz.

The picture on the left hand side shows the Gaussian primes around the origin, with real and imaginary part in [-100,100]. While these primes appear to be quite dense it is an open problem if it is possible to walk from the origin to infinity with steps of size bounded by an absolute constant. (The problem was posed at the International congress of mathematicians in 1962 by Basil Gordon.)

The picture on the right hand side shows the real and imaginary part of the Riemann zeta function zeta(1/2+it) in the complex plane, for t in the range from 0 to 34.