Let C ⊂ Pr be a general curve of genus g embedded via a general linear series of degree d. The well-known Maximal Rank Conjecture asserts that the restriction maps H(OPr(m)) → H(OC(m)) are of maximal rank; if known, this conjecture would determine the Hilbert function of C. In this paper, we prove an analogous statement for the hyperplane sections of general curves. More specifically, if H ⊂ Pr...

Given an elliptic curve E over a number field k, the Galois action on the torsion points of E induces a Galois representation, ρE : Gal(k/k) → GL2(b Z). For a fixed number field k, we describe the image of ρE for a “random” elliptic curve E over k. In particular, if k 6= Q is linearly disjoint from the cyclotomic extension of Q, then ρE will be surjective for “most” elliptic curves over k.

The paper is concerned with the bifurcation of limit cycles in general quadratic perturbations of a quadratic reversible and non-Hamiltonian system, whose period annulus is bounded by an elliptic separatrix related to a singularity at infinity in the poincar'{e} disk. Attention goes to the number of limit cycles produced by the period annulus under perturbations. By using the appropriate Picard...

We construct unramified central simple algebras representing 2-torsion classes in the Brauer group of a hyperelliptic curve, and show that every 2-torsion class can be constructed this way when the curve has a rational Weierstrass point or when the base field is C1. In general, we show that a large (but in general proper) subgroup of the 2torsion classes are given by the construction. Examples ...

In this brief note, we prove the following two Artin-Schreier curves are supersin-gular.

neous (Kay, 1953) or intravenous (Lawrie, Smith & Forrest, 1964) histamine acid phosphate (HAP) and subcutaneous (Makhlouf, McManus & Card, 1966) or intravenous (Konturek & Lankosz, 1967) pentagastrin (ICI 50123). However, similar dose-response curves to determine the minimal dose of a stimulus for maximal pepsin secretion are not reported. In various studies, the doses of different stimuli whi...

Let Ω be a domain in the N -dimensional real space, L be an elliptic differential operator, and (Tn) be a sequence whose members belong to a certain class of operators defined on the space of L-analytic functions on Ω. It is proved in this paper the existence of a dense linear manifold of L-analytic functions all of whose nonzero members have maximal cluster sets under the action of every Tn al...

In this note, we present a simple method for constructing maximal curves defined over Fq2m by the equation yn = T (x), where T (x) is a q-polynomial over Fq2m . © 2004 Elsevier Inc. All rights reserved.

Let k = Fq be a finite field of characteristic 2. A genus 3 curve C/k has many involutions if the group of k-automorphisms admits a C2 × C2 subgroup H (not containing the hyperelliptic involution if C is hyperelliptic). Then C is an ArtinSchreier cover of the three elliptic curves obtained as the quotient of C by the nontrivial involutions of H , and the Jacobian of C is k-isogenous to the prod...

For the Hermitian curve H de ned over the nite eld Fq2 , we give a complete classi cation of Galois coverings of H of prime degree. The corresponding quotient curves turn out to be special cases of wider families of curves Fq2-covered by H arising from subgroups of the special linear group SL(2;Fq) or from subgroups in the normaliser of the Singer group of the projective unitary group PGU(3;Fq2...