On maximal curves having classical Weierstrass gaps

We study geometrical properties of maximal curves having classical Weierstrass gaps.Comment: 9 pages, Latex2

A new tower over cubic finite fields

We present a new explicit tower of function fields (Fn)n≥0 over the finite field with ` = q3 elements, where the limit of the ratios (number of rational places of Fn)/(genus of Fn) is bigger or equal to 2(q2 − 1)/(q + 2). This tower contains as a subtower the tower which was introduced by Bezerra– Garcia–Stichtenoth (see [3]), and in the particular case q = 2 it coincides with the tower of van der Geer–van der Vlugt (see [12]). Many features of the new tower are very similar to those of the optimal wild tower in [8] over the quadratic field Fq2 (whose modularity was shown in [6] by Elkies).

On maximal curves

We study arithmetical and geometrical properties of maximal curves, that is, curves defined over the finite field F_{q^2} whose number of F_{q^2}-rational points reaches the Hasse-Weil upper bound. Under a hypothesis on non-gaps at a rational point, we prove that maximal curves are F_{q^2}-isomorphic to y^q + y = x^m, for some $m \in Z^+$. As a consequence we show that a maximal curve of genus g=(q-1)^2/4 is F_{q^2}-isomorphic to the curve y^q + y = x^{(q+1)/2}.Comment: LaTex2e, 17 pages; this article is an improved version of the paper alg-geom/9603013 (by Fuhrmann and Torres

Towers of Function Fields over Non-prime Finite Fields

Over all non-prime finite fields, we construct some recursive towers of function fields with many rational places. Thus we obtain a substantial improvement on all known lower bounds for Ihara's quantity $A(\ell)$, for $\ell = p^n$ with $p$ prime and $n>3$ odd. We relate the explicit equations to Drinfeld modular varieties

Asymptotics for the genus and the number of rational places in towers of function fields over a finite field

We discuss the asymptotic behaviour of the genus and the number of rational places in towers of function fields over a finite field

Galois towers over non-prime finite fields

In this paper we construct Galois towers with good asymptotic properties over any non-prime finite field $\mathbb F_{\ell}$; i.e., we construct sequences of function fields $\mathcal{N}=(N_1 \subset N_2 \subset \cdots)$ over $\mathbb F_{\ell}$ of increasing genus, such that all the extensions $N_i/N_1$ are Galois extensions and the number of rational places of these function fields grows linearly with the genus. The limits of the towers satisfy the same lower bounds as the best currently known lower bounds for the Ihara constant for non-prime finite fields. Towers with these properties are important for applications in various fields including coding theory and cryptography

An Examination of the Use of Pesticides in Puerto Rican Agriculture

This article examines the overuse of pesticides in Puerto Rican agriculture and its impact on consumer health and the environment. The purpose of this article is to spread awareness about a topic that is unknown to most of the Puerto Rican population, but plays a significant part in citizens’daily lives. It seeks to promote further research into this topic to achieve a deeper understanding of these issues and find sustainable alternatives. The objective is also to promote organic agriculture as an alternative to the current over reliance on industrial methods of agriculture used by biotech companies