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 $G$ be a simple Lie group of real rank at least 2, different than D_4(\bbc), and let $\Gamma$ be any non-uniform lattice of $G$. Let $s_n(\Gamma)$ denote the number of subgroups of index at most $n$ in $\Gamma$. Then the limit $\lim\limits_{n\to \infty} \frac{\log s_n(\Gamma)}{(\log n)^2/ \log \log n}$ exists and equals a constant $\gamma(G)$ which depends only on the Lie type of $G$ and can be easily computed from its root system.Comment: 34 page

METHOD OF TOPICAL DIAGNOSIS OF BRONCHOPLEURAL COMMUNICATIONS IN CHILDREN WITH HEAVY ACUTE PURULENT-DESTRUCTIVE PULMONAL DISEASES

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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 $\Omega \subset \mathbb C$, the Lempert function is a functional on the space Hol (\D,\Omega) of analytic disks with values in $\Omega$, depending on a set of poles in $\Omega$. 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

NEW METHOD OF TEMPORAL OPERATIVE CATHETERIZATION OF TRACHEA AND BRONCHIA OF CHILDREN

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