Statistics for low-lying zeros of symmetric power L-functions in the level aspect

We study one-level and two-level densities for low lying zeros of symmetric power L-functions in the level aspect. It allows us to completely determine the symmetry types of some families of symmetric power L-functions with prescribed sign of functional equation. We also compute the moments of one-level density and exhibit mock-Gaussian behavior discovered by Hughes & Rudnick.Comment: 45 page

General indifference pricing with small transaction costs

We study the utility indifference price of a European option in the context of small transaction costs. Considering the general setup allowing consumption and a general utility function at final time T, we obtain an asymptotic expansion of the utility indifference price as a function of the asymptotic expansions of the utility maximization problems with and without the European contingent claim. We use the tools developed in [54] and [48] based on homogenization and viscosity solutions to characterize these expansions. Finally we study more precisely the example of exponential utilities, in particular recovering under weaker assumptions the results of [6].Comment: 43 page

Statistics for low-lying zeros of symmetric power L-functions in the level aspect

International audienceWe study one-level and two-level densities for low lying zeros of symmetric power L-functions in the level aspect. It allows us to completely determine the symmetry types of some families of symmetric power L-functions with prescribed sign of functional equation. We also compute the moments of one-level density and exhibit mock-Gaussian behavior discovered by Hughes & Rudnick

Lower order terms for the one-level densities of symmetric power LL-functions in the level aspect

International audienceIn a previous paper, the authors determined, among other things, the main terms for the one-level densities for low-lying zeros of symmetric power L-functions in the level aspect. In this paper, the lower order terms of these one-level densities are found. The combinatorial difficulties, which should arise in such context, are drastically reduced thanks to Chebyshev polynomials, which are the characters of the irreducible representations of SU(2).

Le superhéros dans le cinéma étatsunien : approche générique et mythologique

Ce mémoire explore la construction d’un discours mythologique à travers les films de superhéros, dont la production a explosé après les évènements du 11 septembre 2001. La perspective généalogique proposée retrace la figure du superhéros dans les comics des années 1900 pour en suivre l’évolution jusqu’à aujourd’hui dans le cinéma hollywoodien. On montrera comment les évènements du 11 septembre 2001 ont été déterminants dans la production de ce type de films, dont on dégagera les principales caractéristiques : un contenu fortement mythologique, prenant appui sur le mal absolu, et une fonction idéologique, axée principalement sur celle de cohésion sociale. Une étude de cas à partir de Batman relèvera la teneur mythologique et les idéologies présentes dans quatre films, réalisés entre 1943 et 2012. Les écrits de Gérard Bouchard sur le mythe social, ainsi que les thèses de Robert Jewett et John Shelton Lawrence sur le monomythe américain, serviront d’appuis théoriques et critiques à la démonstration de la prégnance de ce type de film dans l’imaginaire cinématographique étatsunien depuis 2001.This essay examines the construction of a mythological discourse by analyzing superhero movies, a genre whose popularity exploded after the terrorist attacks of September 11, 2001. This essay traces back the origins of the superhero figure through the history of the comic book medium in the 20th century all the way to contemporary Hollywood cinema. We will demonstrate how the terrorist attacks have been central to the production of this type of movie, of which we will examine the most important characteristics: a strongly mythological content, supported by a representation of absolute evil, and an ideological function, mainly based on the principle of social cohesion. A case study on the character of Batman will be able to show the mythological content and the ideologies present in four movies, produced between 1943 and 2012. The writings of Gérard Bouchard on the social myth as well as the theories of Robert Jewett and John Shelton Lawrence on the American monomyth will be used to demonstrate the importance of this type of movie in the American culture since 2001