On the cohomology of linear groups over imaginary quadratic fields

Let Gamma be the group GL_N (OO_D), where OO_D is the ring of integers in the imaginary quadratic field with discriminant D<0. In this paper we investigate the cohomology of Gamma for N=3,4 and for a selection of discriminants: D >= -24 when N=3, and D=-3,-4 when N=4. In particular we compute the integral cohomology of Gamma up to p-power torsion for small primes p. Our main tool is the polyhedral reduction theory for Gamma developed by Ash and Koecher. Our results extend work of Staffeldt, who treated the case n=3, D=-4. In a sequel to this paper, we will apply some of these results to the computations with the K-groups K_4 (OO_{D}), when D=-3,-4

Restricted sum formula of alternating Euler sums

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Observation of Collective-Emission-Induced Cooling inside an Optical Cavity

We report the observation of collective-emission-induced, velocity-dependent light forces. One third of a falling sample containing 3 x 10^6 cesium atoms illuminated by a horizontal standing wave is stopped by cooperatively emitting light into a vertically oriented confocal resonator. We observe decelerations up to 1500 m/s^2 and cooling to temperatures as low as 7 uK, well below the free space Doppler limit. The measured forces substantially exceed those predicted for a single two-level atom.Comment: 10 pages, 5 figure

Manipulation of Cold Atomic Collisions by Cavity QED Effects

We show how the dynamics of collisions between cold atoms can be manipulated by a modification of spontaneous emission times. This is achieved by placing the atomic sample in a resonant optical cavity. Spontaneous emission is enhanced by a combination of multiparticle entanglement together with a higher density of modes of the modified vacuum field, in a situation akin to superradiance. A specific situation is considered and we show that this effect can be experimentally observed as a large suppression in trap-loss rates.Comment: RevTex, 2 EPS figures; scheduled for Phys. Rev. Lett. 19 Feb 01, with minor change

Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes

We show how the Hopf algebra structure of multiple polylogarithms can be used to simplify complicated expressions for multi-loop amplitudes in perturbative quantum field theory and we argue that, unlike the recently popularized symbol-based approach, the coproduct incorporates information about the zeta values. We illustrate our approach by rewriting the two-loop helicity amplitudes for a Higgs boson plus three gluons in a simplified and compact form involving only classical polylogarithms.Comment: 46 page

Does the sole description of a tax authority affect tax evasion? The impact of described coercive and legitimate power.

Following the classic economic model of tax evasion, taxpayers base their tax decisions on economic determinants, like fine rate and audit probability. Empirical findings on the relationship between economic key determinants and tax evasion are inconsistent and suggest that taxpayers may rather rely on their beliefs about tax authority’s power. Descriptions of the tax authority’s power may affect taxpayers’ beliefs and as such tax evasion. Experiment 1 investigates the impact of fines and beliefs regarding tax authority’s power on tax evasion. Experiments 2-4 are conducted to examine the effect of varying descriptions about a tax authority’s power on participants’ beliefs and respective tax evasion. It is investigated whether tax evasion is influenced by the description of an authority wielding coercive power (Experiment 2), legitimate power (Experiment 3), and coercive and legitimate power combined (Experiment 4). Further, it is examined whether a contrast of the description of power (low to high power; high to low power) impacts tax evasion (Experiments 2-4). Results show that the amount of fine does not impact tax payments, whereas participants’ beliefs regarding tax authority’s power significantly shape compliance decisions. Descriptions of high coercive power as well as high legitimate power affect beliefs about tax authority’s power and positively impact tax honesty. This effect still holds if both qualities of power are applied simultaneously. The contrast of descriptions has little impact on tax evasion. The current study indicates that descriptions of the tax authority, e.g., in information brochures and media reports, have more influence on beliefs and tax payments than information on fine rates. Methodically, these considerations become particularly important when descriptions or vignettes are used besides objective information

On the cohomology of GL_2 and SL_2 over imaginary quadratic fields

We report on computations of the cohomology of GL_2(O_D) and SL_2(O_D), where D<0 is a fundamental discriminant. These computations go well beyond earlier results of Vogtmann and Scheutzow. We use the technique of homology of Voronoi complexes, and our computations recover the integral cohomology away from the primes 2, 3. We observed exponential growth in the torsion subgroup of H^2 as $D$ increases, and compared our data to bounds of Rohlfs

Building versus maintaining a perceived confidence-based tax climate: experimental evidence

A confidence-based climate between public administrations and citizens is essential. This paper argues and provides empirical evidence that depending on the perceived interaction history, different policies are needed to build versus maintain confidence. Applying the extended Slippery Slope Framework of tax compliance, an online and a laboratory experiment were conducted to explore whether tax authorities’ coercive and legitimate power have different effects depending on whether they are situated in an antagonism-based or confidence-based climate. Results showed that in an antagonism-based interaction climate, a combination of high coercive and high legitimate power changed the climate into a confidence-based interaction climate. In contrast, in a confidence-based climate the same power combination did not maintain but erode the climate. Results also suggest that confidence-based climates are maintained by low coercive power combined with high legitimate power. The paper concludes that interaction climates operate as psychological frames which guide how policy instruments affect taxpayers’ trust in the tax authorities.Social decision makin