L-functions, Generalized modular forms (March, 2011)

  • Generalized modular functions (3 lectures):

  • Generalized modular functions (GMF) are functions holomorphic on the complex upper half plane, meromorphic at the cusps, that satisfy the usual transformation formula of a classical modular function, however with the important exception that the character need not be of finite order (or even unitary). The theory has been partly motivated form CFT in physics. In these three lectures we intend to give a more detailled introduction into the theory, discussing works of Knopp-Mason and two recent papers of Mason and myself.
  • $L$-functions (3 lectures):

  • We intend to discuss basic properties of $L$-functions attached to modular forms, in the one-dimensional and higher-dimensional cases (integral weight, half-integral weight, Siegel modular forms). This includes also $L$-series that do not necessarily have an Euler product.