4,026 research outputs found

    Some genus 3 curves with many points

    Full text link
    Using an explicit family of plane quartic curves, we prove the existence of a genus 3 curve over any finite field of characteristic 3 whose number of rational points stays within a fixed distance from the Hasse-Weil-Serre upper bound. We also provide an intrinsic characterization of so-called Legendre elliptic curves

    Galois Theory, discriminants and torsion subgroups of elliptic curves

    Get PDF
    We find a tight relationship between the torsion subgroup and the image of the mod 2 Galois representation associated to an elliptic curve defined over the rationals. This is shown using some characterizations for the squareness of the discriminant of the elliptic curve.Comment: New version, some typos fixed and the proof of the lemma in the Appendix has been expande

    Extended diffeomorphism algebras in (quantum) gravitational physics

    Full text link
    We construct an explicit representation of the algebra of local diffeomorphisms of a manifold with realistic dimensions. This is achieved in the setting of a general approach to the (quantum) dynamics of a physical system which is characterized by the fundamental role assigned to a basic underlying symmetry. The developed mathematical formalism makes contact with the relevant gravitational notions by means of the addition of some extra structure. The specific manners in which this is accomplished, together with their corresponding physical interpretation, lead to different gravitational models. Distinct strategies are in fact briefly outlined, showing the versatility of the present conceptual framework.Comment: 20 pages, LATEX, no figure

    Effective string picture for confinement at finite temperature: theoretical predictions and high precision numerical results

    Get PDF
    The effective string picture of confinement is used to derive theoretical predictions for the interquark potential at finite temperature. At short distances, the leading string correction to the linear confining potential between a heavy quark-antiquark pair is the "L\"uscher term''. We assume a Nambu--Goto effective string action, and work out subleading contributions in an analytical way. We discuss the contribution given by a possible ``boundary term'' in the effective action, comparing these predictions with results from simulations of lattice Z2Z_2 gauge theory in three dimensions, obtained with an algorithm which exploits the duality of the Z2Z_2 gauge model with the Ising spin model.Comment: Lattice2003(nonzero), 3 pages, 2 figure

    Alternating groups and moduli space lifting Invariants

    Full text link
    Main Theorem: Spaces of r-branch point 3-cycle covers, degree n or Galois of degree n!/2 have one (resp. two) component(s) if r=n-1 (resp. r\ge n). Improves Fried-Serre on deciding when sphere covers with odd-order branching lift to unramified Spin covers. We produce Hurwitz-Torelli automorphic functions on Hurwitz spaces, and draw Inverse Galois conclusions. Example: Absolute spaces of 3-cycle covers with +1 (resp. -1) lift invariant carry canonical even (resp. odd) theta functions when r is even (resp. odd). For inner spaces the result is independent of r. Another use appears in, http://www.math.uci.edu/~mfried/paplist-mt/twoorbit.html, "Connectedness of families of sphere covers of A_n-Type." This shows the M(odular) T(ower)s for the prime p=2 lying over Hurwitz spaces first studied by, http://www.math.uci.edu/~mfried/othlist-cov/hurwitzLiu-Oss.pdf, Liu and Osserman have 2-cusps. That is sufficient to establish the Main Conjecture: (*) High tower levels are general-type varieties and have no rational points.For infinitely many of those MTs, the tree of cusps contains a subtree -- a spire -- isomorphic to the tree of cusps on a modular curve tower. This makes plausible a version of Serre's O(pen) I(mage) T(heorem) on such MTs. Establishing these modular curve-like properties opens, to MTs, modular curve-like thinking where modular curves have never gone before. A fuller html description of this paper is at http://www.math.uci.edu/~mfried/paplist-cov/hf-can0611591.html .Comment: To appear in the Israel Journal as of 1/5/09; v4 is corrected from proof sheets, but does include some proof simplification in \S

    Representations and KK-theory of Discrete Groups

    Full text link
    Let Γ\Gamma be a discrete group of finite virtual cohomological dimension with certain finiteness conditions of the type satisfied by arithmetic groups. We define a representation ring for Γ\Gamma, determined on its elements of finite order, which is of finite type. Then we determine the contribution of this ring to the topological KK-theory K(BΓ)K^*(B\Gamma), obtaining an exact formula for the difference in terms of the cohomology of the centralizers of elements of finite order in Γ\Gamma.Comment: 4 page

    Invariance Properties of Inviscid Fluids of Grade n

    No full text
    Revisited and completed version, 18 pages and 2 figures.International audienceFluids of grade n are continuous media in dynamic changes of phases avoiding the surfaces of discontinuity and representing the capillary layers in liquid-vapour interfaces. We recall the thermodynamic form of the equation of motion for inviscid fluids of grade n. First integrals and theorems of circulation are deduced. A general classification of flows is proposed

    On a differential inclusion related to the Born-Infeld equations

    Get PDF
    We study a partial differential relation that arises in the context of the Born-Infeld equations (an extension of the Maxwell's equations) by using Gromov's method of convex integration in the setting of divergence free fields

    What are the Visual Features Underlying Rapid Object Recognition?

    Get PDF
    Research progress in machine vision has been very significant in recent years. Robust face detection and identification algorithms are already readily available to consumers, and modern computer vision algorithms for generic object recognition are now coping with the richness and complexity of natural visual scenes. Unlike early vision models of object recognition that emphasized the role of figure-ground segmentation and spatial information between parts, recent successful approaches are based on the computation of loose collections of image features without prior segmentation or any explicit encoding of spatial relations. While these models remain simplistic models of visual processing, they suggest that, in principle, bottom-up activation of a loose collection of image features could support the rapid recognition of natural object categories and provide an initial coarse visual representation before more complex visual routines and attentional mechanisms take place. Focusing on biologically plausible computational models of (bottom-up) pre-attentive visual recognition, we review some of the key visual features that have been described in the literature. We discuss the consistency of these feature-based representations with classical theories from visual psychology and test their ability to account for human performance on a rapid object categorization task
    corecore