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Arxiv.org
by Éric Gaudron; Gaël Rémond
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We give a new, sharpened version of the period theorem of Masser and W\"ustholz, which is moreover totally explicit. We also present a new formulation involving all archimedean places. We then derive new bounds for elliptic isogenies, improving those of Pellarin. The small numerical constants obtained allow an application to Serre's uniformity problem in the split Cartan case, thanks to the work of Bilu, Parent and Rebolledo.
Source: http://arxiv.org/abs/1105.1230v1
Arxiv.org
by Eric Marberg
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Diaconis and Isaacs define a supercharacter theory for algebra groups over a finite field by constructing certain unions of conjugacy classes called superclasses and certain reducible characters called supercharacters. This work investigates the properties of algebra subgroups $H\subset G$ which are unions of some set of the superclasses of $G$; we call such subgroups supernormal. After giving a few useful equivalent formulations of this definition, we show that products of supernormal...
Source: http://arxiv.org/abs/1005.4150v4
Arxiv.org
by Jorma Louko; Eric Martinez-Pascual
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We investigate refined algebraic quantisation within a family of classically equivalent constrained Hamiltonian systems that are related to each other by rescaling a momentum-type constraint. The quantum constraint is implemented by a rigging map that is motivated by group averaging but has a resolution finer than what can be peeled off from the formally divergent contributions to the averaging integral. Three cases emerge, depending on the asymptotics of the rescaling function: (i)...
Source: http://arxiv.org/abs/1107.1092v2
Arxiv.org
by Éric Gaudron; Gaël Rémond
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Slopes of an adelic vector bundle exhibit a behaviour akin to successive minima. Comparisons between the two amount to a Siegel lemma. Here we use Zhang's version for absolute minima over the algebraic numbers. We prove a Minkowski-Hlawka theorem in this context. We also study the tensor product of two hermitian bundles bounding both its absolute minimum and maximal slope, thus improving an estimate of Chen. We further include similar inequalities for exterior and symmetric powers, in terms of...
Source: http://arxiv.org/abs/1109.2812v1