Let G be a reductive algebraic group over C and let X be a smooth quasiprojective complex variety. Let us call a representation ρ : π1(X) → G to be G-rigid, if the set theoretic orbit of the representation ρ in the representation space Hom(π1(X), G) under the action of G is an open subset. Note that by fixing an embedding of G into a general linear group GLn(C), any representation ρ : π1(X) → G...

We consider the Fourier expansions of automorphic forms on general Lie groups, with a particular emphasis on exceptional groups. After describing some principles underlying known results on GL(n), Sp(4), and G2, we perform an analysis of the expansions on split real forms of E6 and E7 where simplifications take place for automorphic realizations of real representations which have small Gelfand-...

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In this paper, we give a necessary and sufficient condition for the finiteness of the Galois cohomology of unipotent groups over local fields of positive characteristic. AMS Mathematics Subject Classification (2000): 11E72.

We study eta invariants of Dirac operators and regularized determinants of Dirac Laplacians over hyperbolic manifolds with cusps. We follow Werner Müller (see [18], [19]) and use relative traces to define the eta function and the zeta function. We show regularities of eta and zeta functions at the origin so that we can define the eta invariant and the regularized determinant. By the Selberg tra...