Diophantine approx., arithm. sequences & anal. numb. theory

In contrast to so-called Diophantine equations, where on searches for integer solutions of an equation, the basic question of Diophantine approximation is how well a real number - or a vector of real numbers - can be approximated by a rational number - or by a vector of rational numbers with a common denominator. This question has direct connections to so- called continued fraction expansions and the associated discrete dynamical systems. Diophantine approximation questions appear in number theory in various other contexts, such as with trigonometric products or in the analysis of exponential sums in analytic number theory. The aim of this international project with Russia is to work jointly with teams from Russia and Austria on modern issues from these areas of number theory and to further de velop the theory.

In contrast to so-called Diophantine equations, where one searches for integer solutions of an equation, the basic question of Diophantine approximation is how well a real number - or a vector of real numbers - can be approximated by a rational number - or by a vector of rational numbers with a common denominator. This question has direct connections to so-called continued fraction expansions and the associated discrete dynamical systems. Diophantine approximation questions appear in number theory in various other contexts, such as with trigonometric products or in the analysis of exponential sums in analytic number theory. The aim of this international project with Russia was to work jointly with teams from Russia and Austria on modern issues from these areas of number theory and to further develop the theory. Due to the sanctions on the war between Russia and Ukraine, scientific workshops originally planned as part of the project were not held in Russia and Austria. Nevertheless, almost all of the scientific project goals were achieved.