6,083 research outputs found
Conjectures for the integral moments and ratios of L-functions over function fields
We extend to the function field setting the heuristic previously developed,
by Conrey, Farmer, Keating, Rubinstein and Snaith, for the integral moments and
ratios of -functions defined over number fields. Specifically, we give a
heuristic for the moments and ratios of a family of -functions associated
with hyperelliptic curves of genus over a fixed finite field
in the limit as . Like in the number field
case, there is a striking resemblance to the corresponding formulae for the
characteristic polynomials of random matrices. As an application, we calculate
the one-level density for the zeros of these -functions.Comment: 40 page
Flight test performance and description of a rocket vihicle for producing low-speed artificial meteors
Flight test of trailblazer i reentry vehicle and production of artificial iron meteor
Localization and its consequences for quantum walk algorithms and quantum communication
The exponential speed-up of quantum walks on certain graphs, relative to
classical particles diffusing on the same graph, is a striking observation. It
has suggested the possibility of new fast quantum algorithms. We point out here
that quantum mechanics can also lead, through the phenomenon of localization,
to exponential suppression of motion on these graphs (even in the absence of
decoherence). In fact, for physical embodiments of graphs, this will be the
generic behaviour. It also has implications for proposals for using spin
networks, including spin chains, as quantum communication channels.Comment: 4 pages, 1 eps figure. Updated references and cosmetic changes for v
Method and apparatus for attaching physiological monitoring electrodes Patent
Adhesive spray process for attaching biomedical skin electrode
Attitude determination of the spin-stabilized Project Scanner spacecraft
Attitude determination of spin-stabilized spacecraft using star mapping techniqu
Using Big Bang Nucleosynthesis to Extend CMB Probes of Neutrino Physics
We present calculations showing that upcoming Cosmic Microwave Background
(CMB) experiments will have the power to improve on current constraints on
neutrino masses and provide new limits on neutrino degeneracy parameters. The
latter could surpass those derived from Big Bang Nucleosynthesis (BBN) and the
observationally-inferred primordial helium abundance. These conclusions derive
from our Monte Carlo Markov Chain (MCMC) simulations which incorporate a full
BBN nuclear reaction network. This provides a self-consistent treatment of the
helium abundance, the baryon number, the three individual neutrino degeneracy
parameters and other cosmological parameters. Our analysis focuses on the
effects of gravitational lensing on CMB constraints on neutrino rest mass and
degeneracy parameter. We find for the PLANCK experiment that total (summed)
neutrino mass eV could be ruled out at or better.
Likewise neutrino degeneracy parameters and could be detected or ruled out at
confidence, or better. For POLARBEAR we find that the corresponding detectable
values are , , and , while for EPIC we obtain ,
, and . Our forcast for
EPIC demonstrates that CMB observations have the potential to set constraints
on neutrino degeneracy parameters which are better than BBN-derived limits and
an order of magnitude better than current WMAP-derived limits.Comment: 27 pages, 11 figures, matches published version in JCA
Investigating the Structure of the Windy Torus in Quasars
Thermal mid-infrared emission of quasars requires an obscuring structure that
can be modeled as a magneto-hydrodynamic wind in which radiation pressure on
dust shapes the outflow. We have taken the dusty wind models presented by
Keating and collaborators that generated quasar mid-infrared spectral energy
distributions (SEDs), and explored their properties (such as geometry, opening
angle, and ionic column densities) as a function of Eddington ratio and X-ray
weakness. In addition, we present new models with a range of magnetic field
strengths and column densities of the dust-free shielding gas interior to the
dusty wind. We find this family of models -- with input parameters tuned to
accurately match the observed mid-IR power in quasar SEDs -- provides
reasonable values of the Type 1 fraction of quasars and the column densities of
warm absorber gas, though it does not explain a purely luminosity-dependent
covering fraction for either. Furthermore, we provide predictions of the
cumulative distribution of E(B-V) values of quasars from extinction by the wind
and the shape of the wind as imaged in the mid-infrared. Within the framework
of this model, we predict that the strength of the near-infrared bump from hot
dust emission will be correlated primarily with L/L_Edd rather than luminosity
alone, with scatter induced by the distribution of magnetic field strengths.
The empirical successes and shortcomings of these models warrant further
investigations into the composition and behaviour of dust and the nature of
magnetic fields in the vicinity of actively accreting supermassive black holes.Comment: 11 pages, 6 figures, accepted for publication in MNRA
Random Matrix Theory and the Fourier Coefficients of Half-Integral Weight Forms
Conjectured links between the distribution of values taken by the
characteristic polynomials of random orthogonal matrices and that for certain
families of L-functions at the centre of the critical strip are used to
motivate a series of conjectures concerning the value-distribution of the
Fourier coefficients of half-integral weight modular forms related to these
L-functions. Our conjectures may be viewed as being analogous to the Sato-Tate
conjecture for integral weight modular forms. Numerical evidence is presented
in support of them.Comment: 28 pages, 8 figure
Autocorrelation of Random Matrix Polynomials
We calculate the autocorrelation functions (or shifted moments) of the
characteristic polynomials of matrices drawn uniformly with respect to Haar
measure from the groups U(N), O(2N) and USp(2N). In each case the result can be
expressed in three equivalent forms: as a determinant sum (and hence in terms
of symmetric polynomials), as a combinatorial sum, and as a multiple contour
integral. These formulae are analogous to those previously obtained for the
Gaussian ensembles of Random Matrix Theory, but in this case are identities for
any size of matrix, rather than large-matrix asymptotic approximations. They
also mirror exactly autocorrelation formulae conjectured to hold for
L-functions in a companion paper. This then provides further evidence in
support of the connection between Random Matrix Theory and the theory of
L-functions
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