Research Projects

Current Projects

Diophantine Number Theory

In this joint project of the FWF and the NKFIH we shall use different techniques from Diophantine number theory (as the subspace theorem, the theory of linear forms in logarithms, Runge’s method, hypergeometric methods, etc.) to study various Diophantine problems. E.g. we work on Ritt’s decomposition theory and Diophantine applications, we shall study some classical Diophantine equations (as the Erdös-Straus conjecture, Goormaghtigh’s equation and the generalized Ramanujan-Nagell equation, Thue and relative Thue equations), and we shall investigate Diophantine problems with recurrence sequences. We emphasize that the Austrian and Hungarian research groups have a long standing and very fruitful cooperation, which is exceptional even by the international standards. Through this project we want to maintain this tight scientific bond and in particular encourage collaboration between younger members of the groups. The project has started on 01.04.2020. (Clemens Fuchs)

Former Projects

Arithmetic Primitives for Uniform Distribution Modulo 1

This project is about techniques relevant for the theory of uniform distribution modulo 1 of sequences and its applications in the field of random number generation and quasi‐Monte Carlo methods. It is funded by the FWF Austrian Science Fund and started in February 2014. (Peter Hellekalek)

EMMA – Experimentieren mit mathematischen Algorithmen

A cooperative project between the Department of Mathematics, University of Salzburg and the HTL Braunau. (Clemens Fuchs, Karl-Josef Fuchs, Wolfgang Schmid, Andreas Schröder)

  • Further information: EMMA

Explicit Problems in Diophantine Analysis and Geometry

The project is funded by the FWF Austrian Science Fund and started 2012. The place of research was initially at the Institute for Analysis and Computational Number Theory (Math A), TU Graz. The project was shifted to the Department of Mathematics, University of Salzburg in 2013. (Clemens Fuchs)

Diophantine equations, arithmetic progressions and their applications

The unit sum problem concerns the following question: Which number fields have the property that their rings of integers are generated by its group of units. Here, methods of Diophantine analysis, the theory of development of digits, and symbolic computation can be used. During this project the above mentioned methods also should be extended. (Volker Ziegler)