# Joachim Mahnkopf

**Homepage:** -

**Fields of interest:**

*(1)* Special values of automorphic
L-functions: The Deligne conjecture predicts the special values of
**L**-functions at critical points. In our work we deal with the analogou of
Deligne's conjecture for Automorphic L-functions.
*(2)* P-adic families of automorphic forms: The Mazur-Gouvea Conjecture
roughly asserts that any modular form fits into a **p**-adic analytic
family of modular forms. In the case of ordinary forms this is Hida's
theory, in general it has been proven by Coleman. In our work we want to
introduce a new approach to the theory which is based on the trace
formula.

**Selected publications**

*Cohomology of arithmetic groups, Parabolic subgroups and the special values of automorphic L-functions*, J. Inst. Math. de Jussieu, 4 (2005), 553-637.*Trace on Hecke algebras and*, (preprint) [PDF]**p**-adic families of modular forms*On truncation of irreducible representations of Chevalley groups*, J. Number theory 133 (2013)*On truncation of irreducible Chevalley groups II*, J. Number theory 143 (2014)*On truncation of irreducible representations of Chevalley groups III*, preprint