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