Paula Lins de Araujo was one of the main speakers at an international spring school in Germany

Paula Lins de Araujo was one of the main speakers at an international spring school in Germany

Lincoln algebraist Paula Lins de Araujo was invited to be one of the four main lecturers at a pure mathematics event in Germany, at the University of Göttingen. The event was called RTG2491 Spring School “Zeta functions, dynamics and analytic number theory” was meant to introduce young researchers (PhDs and early career Postdocs) to different aspects of zeta functions. Paula gave a series of lectures on Dirichlet series and zeta functions of groups.

Abstract: The Riemann zeta function is a complex function that has become famous because of its connection with the distribution of prime numbers and the Riemann Hypothesis, a conjecture considered by many the most important unsolved problem in pure mathematics. The Riemann zeta function is a particular case of a Dirichlet series, which are series encoding arithmetic information of certain mathematical objects. In particular, one can define a Dirichlet series encoding information of groups. This allows one to recover group theoretical properties by investigating analytical properties of the Dirichlet series, in a similar way we can recover information about primes by looking at an analytical property of the Riemann zeta function. In this mini course, Dirichlet series and zeta functions of groups will be introduced. We will cover basic properties, including abscissa of convergence, growth types and Euler decompositions.