104 research outputs found
Numerical evidence toward a 2-adic equivariant ''Main Conjecture''
International audienceWe test a conjectural non abelian refinement of the classical 2-adic Main Conjecture of Iwasawa theory. In the first part, we show how, in the special case that we study, the validity of this refinement is equivalent to a congruence condition on the coefficients of some power series. Then, in the second part, we explain how to compute the first coefficients of this power series and thus numerically check the conjecture in that setting
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
Planck Intermediate Results II: Comparison of Sunyaev–Zeldovich measurements from Planck and from the Arcminute Microkelvin Imager for 11 galaxy clusters
A comparison is presented of Sunyaev–Zeldovich measurements for 11 galaxy clusters as obtained by Planck and by the ground-based interferom- eter, the Arcminute Microkelvin Imager. Assuming a universal spherically-symmetric Generalised Navarro, Frenk & White (GNFW) model for the cluster gas pressure profile, we jointly constrain the integrated Compton-Y parameter (Y500) and the scale radius (θ500) of each cluster. Our resulting constraints in the Y500 − θ500 2D parameter space derived from the two instruments overlap significantly for eight of the clusters, although, overall, there is a tendency for AMI to find the Sunyaev–Zeldovich signal to be smaller in angular size and fainter than Planck. Significant discrepancies exist for the three remaining clusters in the sample, namely A1413, A1914, and the newly-discovered Planck cluster PLCKESZ G139.59+24.18. The robustness of the analysis of both the Planck and AMI data is demonstrated through the use of detailed simulations, which also discount confusion from residual point (radio) sources and from diffuse astrophysical foregrounds as possible explanations for the discrepancies found. For a subset of our cluster sample, we have investigated the dependence of our results on the assumed pressure profile by repeating the analysis adopting the best-fitting GNFW profile shape which best matches X-ray observations. Adopting the best-fitting profile shape from the X-ray data does not, in general, resolve the discrepancies found in this subset of five clusters. Though based on a small sample, our results suggest that the adopted GNFW model may not be sufficiently flexible to describe clusters universally
Planck intermediate results I : Further validation of new Planck clusters with XMM-Newton
Peer reviewe
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
Charge-dependent flow and the search for the chiral magnetic wave in Pb-Pb collisions at root s(NN)=2.76 TeV
Peer reviewe
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