Doktorandseminarium: An application of adeles

  • Datum:
  • Plats: Ångströmlaboratoriet 64119
  • Föreläsare: Gustav Hammarhjelm
  • Kontaktperson: Volodymyr Mazorchuk
  • Seminarium

Abstract:

In my talk I will define the field of p-adic numbers, show that it is a locally compact group (LCG) and consider one of its corresponding Haar measures. Then another LCG, the ring of rational adeles, will be defined. The adeles provide a framework for describing the set of visible points in the d-dimensional integer lattice as a cut-and-project set. This description is then used in a short proof of the fact that the density of  visible points in the d-dimensional integer lattice is 1/z(d), where z is the Riemann zeta function.