4,541 research outputs found
Curves of genus 3 over small finite fields
We present a table containing the maximal number of rational points on a
genus 3 curve over a field of cardinality q, for all q<100. Also, some remarks
on Frobenius non-classical quartics over finite fields are given.Comment: 9 page
A singular K3 surface related to sums of consecutive cubes
We study the surface arising from the diophantine equation
. It turns out that this is a surface with
Picard number 20. We stduy its aritmetic properties in detail. We construct
elliptic fibrations on it, and we find a parametric solution to the original
equation. Also, we determine the Hasse-Weil zeta function of the surface over
Legendre elliptic curves over finite fields
We show that every elliptic curve over a finite field of odd characteristic
whose number of rational points is divisible by 4 is isogenous to an elliptic
curve in Legendre form, with the sole exception of a minimal respectively
maximal elliptic curve. We also collect some results concerning the
supersingular Legendre parameters
Catabolic mobile genetic elements and their potential use in bioaugmentation of polluted soils and waters
Relaxation behaviour at the spin-flop phase transition in the quasi-1D antiferromagnet CsMnCl3·2H2O
The low-frequency relaxation behaviour of the linear-chain antiferromagnet CsMnCl3·2H2O at the spin-flop transition has been determined from dynamic susceptibility measurements on a single crystal placed in direct contact with liquid helium. The experiments were performed between 1.4 and 4.2 K in the frequency range 0.1 Hz–3.0 kHz with a frequency-sweeping SQUID susceptometer. Below Tλ = 2.17 K, the relaxation rate τ−1 manifests an exponential temperature dependence, τ−1 = ω0e−E/kT, where E/k = 3.19±0.04 K is approximately equal to the magnitude of the intrachain exchange interaction constant Ja/k. Above Tλ the apparent deviation from the exponential behaviour has been explained satisfactorily by using the thermal conduction model of relaxation. The field-dependent factor ω0 is directly proportional to the ratio of the adiabatic χs to the isothermal χT susceptibilities
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