Note sur une formule de M. Schoute

Rendiconti del Circolo Matematico di Palermo Series 1 -     

Remarque sur une formule de Shimura-Taniyama

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Sur une formule fondamentale de Kronecker

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Sur une extension de la formule de Stirling

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Intégrales-fibres pour une formule de Chowla - Selberg

The Chowla-Selberg formula links the class number of negative fundamental quadratic discriminant to values of the Dedekind eta function evaluated over representatives of the class group. It enables the explicit calculation of a large class of elliptic integrals, especially the complete elliptic integrals of the first kind. In this work, we use the integral-fibre theory to offer a new proof of a significant case of this fundamental formula. The method we present here seems susceptible of getting a direct analytic access to a generalization of the explicit instances of the Chowla-Selberg formula in higher dimensions.     

Une démonstration simplifiée et une extension de la formule d'Abramov sur l'entropie des transformations induites

Summary Abramov's formula on the entropy of induced automorphisms is simplified and extended to random powers of automorphisms.

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Equipe de recherche n 1 «< Processus stochastiques et applications»>, dépendant de la section n 2 «, associée au C.N.R.S.     

Systeme de poids sur une algebre de Lie nilpotente

Let g be anilpotent Lie algebra (of finite dimensionn over an algebraically closed field of characteristic zero) and let Der(g) be the algebra of derivations of g. Thesystem of weights of g is defined as being that of the standard representation of a maximal torus in Der(g) (see l.l). For a fixed integern, it is well-known that there are in general uncountably many isomorphism classes of nilpotent Lie algebra of dimensionn; but we show that there arefinitely many systems of weights, and each of them is explicitely constructed. The class of those Lie algebras having a given (arbitrary) system of weights is also studied.The first chapter is a setting for the study of nilpotent Lie algebras, used to prove some general theorems. In the second chapter, attention is restricted to a class of nilpotent Lie algebras for which our setting is particularly well adapted.

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Ce papier est extrait de mon travail de thèse [5] effectué sous la direction du Professeur Jean de Siebenthal que je remercie vivement.     

Sur une conjecture de M. Kac

Summary We consider the following heat conduction problem. Let K be a compact set in Euclidean space ³. Suppose that K is held at the temperature 1, while the surrounding medium is at the temperature 0 at time 0. Following Spitzer we investigate the asymptotic behaviour of the integral E _K (t) which represents the total energy flow in time t from the set K to the surrounding medium ³–K. An asymptotic expansion is given for E _K (t) which refines a theorem due to Spitzer. This expansion also verifies and improves a formal calculation of Kac. Similar results are proved in higher dimensions. Up to the constant m(K), the quantity E _K (t) can be interpreted as the expected value of the volume of the Wiener sausage associated with K and a d-dimensional Brownian motion. This point of view both plays a major role in the proofs and leads to a probabilistic interpretation of the different terms of the expansion.     

Semi-martingales indexées par une partie de ℝd et formule de lto. Cas continu

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Spectre d'anneaux de polynômes sur une suite de modules

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Note sur les formules de saut de Guillemin–Kalkman

The purpose of this Note is to give a jump formula in equivariant cohomology implying the jump formulas of Guillemin–Kalkman. To cite this article: P.-É. Paradan, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Note sur la decomposition de Kℵ0

This note provides a simple counterexample to the following conjecture of Nash-Williams [1]: let T be a denumerably infinite tree; then the complete graph on ?₀ vertices has a T-decomposition if and only if T has no cofinite vertex.     

Fibrés vectoriels semi-stables sur une courbe de Mumford

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