2,074 research outputs found
Subgroup growth of lattices in semisimple Lie groups
We give very precise bounds for the congruence subgroup growth of arithmetic
groups. This allows us to determine the subgroup growth of irreducible lattices
of semisimple Lie groups. In the most general case our results depend on the
Generalized Riemann Hypothesis for number fields but we can state the following
unconditional theorem:
Let be a simple Lie group of real rank at least 2, different than
D_4(\bbc), and let be any non-uniform lattice of . Let
denote the number of subgroups of index at most in .
Then the limit exists and equals a constant which depends only on
the Lie type of and can be easily computed from its root system.Comment: 34 page
Essays on fiscal sustainability in Europe
Fiscal sustainability is present when the current government debt equates to the present
value of future budget surpluses or their excess over deficits but since 1970 the EU
countries on average had a surplus budget only in one year. The first aim of the thesis is to
see whether Europe has achieved fiscal sustainability, whereas the second aim is to analyse
the effects of Maastricht and the Stability and Growth Pact to this end. Another research
aim is to present a formal fiscal sustainability assessment for the EU accession countries.
Finally, the thesis bridges fiscal and external sustainability and studies the economy-wide
sustainability separately in 'old' Europe and the accession countries. [Continues.
Convergence and multiplicities for the Lempert function
Given a domain , the Lempert function is a
functional on the space Hol (\D,\Omega) of analytic disks with values in
, depending on a set of poles in . We generalize its definition
to the case where poles have multiplicities given by local indicators (in the
sense of Rashkovskii's work) to obtain a function which still dominates the
corresponding Green function, behaves relatively well under limits, and is
monotonic with respect to the indicators. In particular, this is an improvement
over the previous generalization used by the same authors to find an example of
a set of poles in the bidisk so that the (usual) Green and Lempert functions
differ.Comment: 24 pages; many typos corrected thanks to the referee of Arkiv for
Matemati
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