122 research outputs found
Root multiplicities and number of nonzero coefficients of a polynomial
It is known that the weight (that is, the number of nonzero coefficients) of
a univariate polynomial over a field of characteristic zero is larger than the
multiplicity of any of its nonzero roots. We extend this result to an
appropriate statement in positive characteristic. Furthermore, we present a new
proof of the original result, which produces also the exact number of monic
polynomials of a given degree for which the bound is attained. A similar
argument allows us to determine the number of monic polynomials of a given
degree, multiplicity of a given nonzero root, and number of nonzero
coefficients, over a finite field of characteristic larger than the degree.Comment: 6 pages. Minor change from previous version: added Example 6,
illustrating the difficulties arising when one tries to relax the hypothesis
n<p of Theorem
Covering theorems for Artinian rings
The covering properties of Artinian rings which depend on their additive structure only, are investigated
Counting and effective rigidity in algebra and geometry
The purpose of this article is to produce effective versions of some rigidity
results in algebra and geometry. On the geometric side, we focus on the
spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic
hyperbolic 2-manifolds (resp., 3-manifolds). By work of Reid, this spectrum
determines the commensurability class of the 2-manifold (resp., 3-manifold). We
establish effective versions of these rigidity results by ensuring that, for
two incommensurable arithmetic manifolds of bounded volume, the length sets
(resp., the complex length sets) must disagree for a length that can be
explicitly bounded as a function of volume. We also prove an effective version
of a similar rigidity result established by the second author with Reid on a
surface analog of the length spectrum for hyperbolic 3-manifolds. These
effective results have corresponding algebraic analogs involving maximal
subfields and quaternion subalgebras of quaternion algebras. To prove these
effective rigidity results, we establish results on the asymptotic behavior of
certain algebraic and geometric counting functions which are of independent
interest.Comment: v.2, 39 pages. To appear in Invent. Mat
Search for a new gauge boson in the Experiment (APEX)
We present a search at Jefferson Laboratory for new forces mediated by
sub-GeV vector bosons with weak coupling to electrons. Such a
particle can be produced in electron-nucleus fixed-target scattering and
then decay to an pair, producing a narrow resonance in the QED trident
spectrum. Using APEX test run data, we searched in the mass range 175--250 MeV,
found no evidence for an reaction, and set an upper limit of
. Our findings demonstrate that fixed-target
searches can explore a new, wide, and important range of masses and couplings
for sub-GeV forces.Comment: 5 pages, 5 figures, references adde
The G0 Experiment: Apparatus for Parity-Violating Electron Scattering Measurements at Forward and Backward Angles
In the G0 experiment, performed at Jefferson Lab, the parity-violating
elastic scattering of electrons from protons and quasi-elastic scattering from
deuterons is measured in order to determine the neutral weak currents of the
nucleon. Asymmetries as small as 1 part per million in the scattering of a
polarized electron beam are determined using a dedicated apparatus. It consists
of specialized beam-monitoring and control systems, a cryogenic hydrogen (or
deuterium) target, and a superconducting, toroidal magnetic spectrometer
equipped with plastic scintillation and aerogel Cerenkov detectors, as well as
fast readout electronics for the measurement of individual events. The overall
design and performance of this experimental system is discussed.Comment: Submitted to Nuclear Instruments and Method
A Measurement of the Electric Form Factor of the Neutron through at (GeV/c)
We report the first measurement of the neutron electric form factor
via using a solid polarized target. was
determined from the beam-target asymmetry in the scattering of longitudinally
polarized electrons from polarized deuterated ammonia, ND. The
measurement was performed in Hall C at Thomas Jefferson National Accelerator
Facility (TJNAF) in quasi free kinematics with the target polarization
perpendicular to the momentum transfer. The electrons were detected in a
magnetic spectrometer in coincidence with neutrons in a large solid angle
segmented detector. We find at (GeV/c).Comment: Latex2e 5 pages, 3 figure
Measurement of Tensor Polarization in Elastic Electron-Deuteron Scattering at Large Momentum Transfer
Tensor polarization observables (t20, t21 and t22) have been measured in
elastic electron-deuteron scattering for six values of momentum transfer
between 0.66 and 1.7 (GeV/c)^2. The experiment was performed at the Jefferson
Laboratory in Hall C using the electron HMS Spectrometer, a specially designed
deuteron magnetic channel and the recoil deuteron polarimeter POLDER. The new
data determine to much larger Q^2 the deuteron charge form factors G_C and G_Q.
They are in good agreement with relativistic calculations and disagree with
pQCD predictions.Comment: 5 pages, 4 figures, for associated informations, see
http://isnwww.in2p3.fr/hadrons/t20/t20_ang.html clarification about several
topics, one figure has been had, extraction of form factors use AQ
interpolation in our Q2 range onl
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