This is connected with properties of the Fourier coefficients of certain Theta series. In a very recent developement it became apparent that Theta series also have applications in the valuation of exotic options. Here they determine in particular the structural properties of the double-barrier options. These allow to reconstruct the information even if errors occured during its transmission. The class of selfdual even codes is of particular interest.
Abelian varieties are of fundamental importance in geometry and number theory.
The set of all Abelian varieties is parametrized by a particular modular space. Modular spaces of this origin are typical examples of Shimura varieties. These in turn are objects of both an analytical and an arithmetical nature. Their arithmetical properties are studied by methods of algebraic geometry, in particular the etale cohomology. Some particularly interesting and important classes of Shimura varieties have height functions that are defined via arithmetic intersection theory.