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This paper contains both theoretical results and experimental data on the behavior of the dimensions of the cohomology spaces H(Γ, En), where Γ is a lattice in SL(2,C) and En = Sym n ⊗Symn, n ∈ N ∪ {0}, is one of the standard self-dual modules. In the case Γ = SL(2,O) for the ring of integers O in an imaginary quadratic number field, we make the theory of… (More)

- Tobias Finis, Erez M Lapid, Werner Müller
- Proceedings of the National Academy of Sciences…
- 2009

The trace formula is one of the most important tools in the theory of automorphic forms. It was invented in the 1950's by Selberg, who mostly studied the case of hyperbolic surfaces, and was later on developed extensively by Arthur in the generality of an adelic quotient of a reductive group over a number field. Here we provide an explicit expression for… (More)

- TOBIAS FINIS, EREZ LAPID
- 2007

We derive a refinement of the spectral expansion of Arthur’s trace formula. The expression is absolutely convergent with respect to the trace norm.

- Tobias Finis, Fritz Grunewald, Paulo Tirao
- Experimental Mathematics
- 2010

- TOBIAS FINIS, EREZ LAPID
- 2016

We provide a uniform estimate for the L-norm (over any interval of bounded length) of the logarithmic derivatives of global normalizing factors associated to intertwining operators for the following reductive groups over number fields: inner forms of GL(n); quasi-split classical groups and their similitude groups; the exceptional group G2. This estimate is… (More)

- TOBIAS FINIS, EREZ LAPID
- 2013

We study the exactness of certain combinatorially defined complexes which generalize the Orlik-Solomon algebra of a geometric lattice. The main results pertain to complex reflection arrangements and their restrictions. In particular, we consider the corresponding relation complexes and give a simple proof of the n-formality of these hyperplane arrangements.… (More)

- TOBIAS FINIS, Atsushi Ichino, Taku Ishii
- 2013

We review some recent joint work of the author with E. Lapid and W. Müller on the limit multiplicity problem for congruence subgroups of arithmetic lattices in the case of non-compact quotients.

- TOBIAS FINIS, EREZ LAPID
- 2008

Let V be a real vector space of dimension d and V ∗ its dual space. By a cone in V ∗ we will always mean a closed polyhedral cone σ with apex 0 such that σ ∩ −σ = {0}. Let Σ be a fan in V ∗, i.e., a collection of cones such that (1) if σ ∈ Σ then any face of σ belongs to Σ, (2) if σ1, σ2 ∈ Σ then σ1 ∩ σ2 is a face in both. We will assume that Σ is complete,… (More)

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