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 $m^3+(m+1)^3+...+(m+k-1)^3=l^2$. It turns out that this is a $K3$ 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 $Q$

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

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