A realization of the Hecke algebra on the space of period functions for Gamma_0(n)

The standard realization of the Hecke algebra on classical holomorphic cusp forms and the corresponding period polynomials is well known. In this article we consider a nonstandard realization of the Hecke algebra on Maass cusp forms for the Hecke congruence subgroups Gamma_0(n). We show that the vector valued period functions derived recently by Hilgert, Mayer and Movasati as special eigenfunctions of the transfer operator for Gamma_0(n) are indeed related to the Maass cusp forms for these groups. This leads also to a simple interpretation of the ``Hecke like'' operators of these authors in terms of the aforementioned non standard realization of the Hecke algebra on the space of vector valued period functions.Comment: 30 pages; corrected typos and fixed incomplete proofs in section

Growing Massive Black Hole Pairs in Minor Mergers of Disk Galaxies

We perform a suite of high-resolution smoothed particle hydrodynamics simulations to investigate the orbital decay and mass evolution of massive black hole (MBH) pairs down to scales of ~30 pc during minor mergers of disk galaxies. Our simulation set includes star formation and accretion onto the MBHs, as well as feedback from both processes. We consider 1:10 merger events starting at z~3, with MBH masses in the sensitivity window of the Laser Interferometer Space Antenna, and we follow the coupling between the merger dynamics and the evolution of the MBH mass ratio until the satellite galaxy is tidally disrupted. While the more massive MBH accretes in most cases as if the galaxy were in isolation, the satellite MBH may undergo distinct episodes of enhanced accretion, owing to strong tidal torques acting on its host galaxy and to orbital circularization inside the disk of the primary galaxy. As a consequence, the initial 1:10 mass ratio of the MBHs changes by the time the satellite is disrupted. Depending on the initial fraction of cold gas in the galactic disks and the geometry of the encounter, the mass ratios of the MBH pairs at the time of satellite disruption can stay unchanged or become as large as 1:2. Remarkably, the efficiency of MBH orbital decay correlates with the final mass ratio of the pair itself: MBH pairs that increase significantly their mass ratio are also expected to inspiral more promptly down to nuclear-scale separations. These findings indicate that the mass ratios of MBH pairs in galactic nuclei do not necessarily trace the mass ratios of their merging host galaxies, but are determined by the complex interplay between gas accretion and merger dynamics.Comment: 5 pages, 4 figures, replaced to match accepted version on Ap

Employment restructuring and flexibility in Austrian and Danish banking

The literature on the impact of new competitive forces on ‘traditional’ industries in Europe tends to emphasize a rather unidirectional line of development. Concentration of capital will pave the way for structural adaptation leading to rationalization and redundancies. In contrast, this cross-national study of the Austrian and Danish banking industries, which have very much in common in terms of their contextual characteristics, indicates rather diverse approaches to pressures for change. Even though competitive pressures are similar, differences in employment restructuring and flexibility prevail between the two national sectors

Rapid Formation of Supermassive Black Hole Binaries in Galaxy Mergers with Gas

Supermassive black holes (SMBHs) are a ubiquitous component of the nuclei of galaxies. It is normally assumed that, following the merger of two massive galaxies, a SMBH binary will form, shrink due to stellar or gas dynamical processes and ultimately coalesce by emitting a burst of gravitational waves. However, so far it has not been possible to show how two SMBHs bind during a galaxy merger with gas due to the difficulty of modeling a wide range of spatial scales. Here we report hydrodynamical simulations that track the formation of a SMBH binary down to scales of a few light years following the collision between two spiral galaxies. A massive, turbulent nuclear gaseous disk arises as a result of the galaxy merger. The black holes form an eccentric binary in the disk in less than a million years as a result of the gravitational drag from the gas rather than from the stars.Comment: Accepted for publication in Science, 40 pages, 7 figures, Supplementary Information include

Welfare and Trade without Pareto

Head, Keith Mayer, Thierry Thoenig, Mathias Welfare and Trade without Pareto American Economic Review 104 5 310-16 2014 10.1257/aer.104.5.310 https://www.aeaweb.org/articles?id=10.1257/aer.104.5.31