A conjectural Lefschetz formula for locally symmetric spaces

We formulate a conjectural Lefschetz formula for locally symmetric spaces of finite volume. The formula can be verified in the compact case and for Riemann surfaces.Comment: LaTeX, 18 page

A general tensor product theorem

We show that every admissible irreducible representation of a product of two locally compact groups is a tensor product of admissible irreducible representations of the factors

A semi-local trace identity and the Riemann hypothesis for function fields

The asymptotic trace formula of A. Connes is restated in a semi-local form, thus showing that the difficulties in giving a direct proof do not lie in the change of topology when transgressing from finitely many places to infinitely many.Comment: LATEX 19 page

The Ihara-Selberg zeta function for PGL(3) and Hecke operators

We prove an approximation to an Ihara-formula for the zeta function of an arithmetic quotient of the Bruhat-Tits building of a p-adic PGL(3).Comment: LaTeX, 14 pages, 1 pictur

A simple trace formula for arithmetic groups

We deduce from Arthur's trace formula a formula with only orbital integrals on the geometric side.Comment: Latex 17 page

Equivariant torsion of locally symmetric spaces

The equivariant holomorphic torsion of a compact locally symmetric manifold and an automorphism is expressed as a special value of a zeta function built out of geometric data (closed geodesics) of the manifold.Comment: LATEX, 24 page

Holomorphic torsion for Hermitian locally symmetric spaces

The holomorphic torsion of a compact locally symmetric manifold is expressed as a special value of a zeta function built out of geometric data (closed geodesics) of the manifold.Comment: LATEX, 29 page

Lewis-Zagier correspondence for higher order forms

The Lewis-Zagier correspondence, which attaches period functions to Maa\ss\ wave forms, is extended to wave forms of higher order, which are higher invariants of the Fuchsian group in question. The key ingredient is an identification of Higher order invariants with ordinary invariants of unipotent twists. This makes it possible to apply standard methods of automorphic forms to higher order forms

Belian categories

We instal homological algebra, including derived functors, on certain non-additive categories like categories of pointed CW-complexes, modules of monoids or sheaves thereof. We apply this theory to Monoid schemes and sheaves on them, compare the result with the base change and prove several structural theorems

Regularized and L2L^2-Determinants

It is shown that in a tower of coverings the regularized determinant of a generalized Laplacian converges to the $L^2$-determinant. This shows generic nontriviality of analytic torsion or regularized determinants since the $L^2$-counterparts are easier to compute. We further have an "Euler product expansion" for regularized determinants in terms of equivariant $L^2$-determinants.Comment: LATEX, 30 page