## L-functions, Generalized modular forms (17th - 22nd March, 2011)

### W. Kohnen

Abstract:

"Generalized modular functions" (1 and 1/2 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" (1 and 1/2 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.