83 research outputs found
Amicable pairs and aliquot cycles for elliptic curves
An amicable pair for an elliptic curve E/Q is a pair of primes (p,q) of good
reduction for E satisfying #E(F_p) = q and #E(F_q) = p. In this paper we study
elliptic amicable pairs and analogously defined longer elliptic aliquot cycles.
We show that there exist elliptic curves with arbitrarily long aliqout cycles,
but that CM elliptic curves (with j not 0) have no aliqout cycles of length
greater than two. We give conjectural formulas for the frequency of amicable
pairs. For CM curves, the derivation of precise conjectural formulas involves a
detailed analysis of the values of the Grossencharacter evaluated at a prime
ideal P in End(E) having the property that #E(F_P) is prime. This is especially
intricate for the family of curves with j = 0.Comment: 53 page
Elliptic flow of charged particles in Pb-Pb collisions at 2.76 TeV
We report the first measurement of charged particle elliptic flow in Pb-Pb
collisions at 2.76 TeV with the ALICE detector at the CERN Large Hadron
Collider. The measurement is performed in the central pseudorapidity region
(||<0.8) and transverse momentum range 0.2< < 5.0 GeV/. The
elliptic flow signal v, measured using the 4-particle correlation method,
averaged over transverse momentum and pseudorapidity is 0.087 0.002
(stat) 0.004 (syst) in the 40-50% centrality class. The differential
elliptic flow v reaches a maximum of 0.2 near = 3
GeV/. Compared to RHIC Au-Au collisions at 200 GeV, the elliptic flow
increases by about 30%. Some hydrodynamic model predictions which include
viscous corrections are in agreement with the observed increase.Comment: 10 pages, 4 captioned figures, published version, figures at
http://aliceinfo.cern.ch/ArtSubmission/node/389
Higher harmonic anisotropic flow measurements of charged particles in Pb-Pb collisions at 2.76 TeV
We report on the first measurement of the triangular , quadrangular
, and pentagonal charged particle flow in Pb-Pb collisions at 2.76
TeV measured with the ALICE detector at the CERN Large Hadron Collider. We show
that the triangular flow can be described in terms of the initial spatial
anisotropy and its fluctuations, which provides strong constraints on its
origin. In the most central events, where the elliptic flow and
have similar magnitude, a double peaked structure in the two-particle azimuthal
correlations is observed, which is often interpreted as a Mach cone response to
fast partons. We show that this structure can be naturally explained from the
measured anisotropic flow Fourier coefficients.Comment: 10 pages, 4 figures, published version, figures at
http://aliceinfo.cern.ch/ArtSubmission/node/387
Measurement of D+- and D0 production in deep inelastic scattering using a lifetime tag at HERA
The production of D-+/-- and D-0-mesons has been measured with the ZEUS detector at HERA using an integrated luminosity of 133.6 pb(-1). The measurements cover the kinematic range 5 < Q(2) < 1000 GeV2, 0.02 < y < 0.7, 1.5 < p(T)(D) < 15 GeV and |eta(D)| < 1.6. Combinatorial background to the D-meson signals is reduced by using the ZEUS microvertex detector to reconstruct displaced secondary vertices. Production cross sections are compared with the predictions of next-to-leading-order QCD, which is found to describe the data well. Measurements are extrapolated to the full kinematic phase space in order to obtain the open-charm contribution, F-2(c (c) over bar), to the proton structure function, F-2
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