On the Deuring Polynomial for Drinfeld Modules in Legendre Form

We study a family $\psi^{\lambda}$ of $\mathbb F_q[T]$-Drinfeld modules, which is a natural analog of Legendre elliptic curves. We then find a surprising recurrence giving the corresponding Deuring polynomial $H_{p(T)}(\lambda)$ characterising supersingular Legendre Drinfeld modules $\psi^{\lambda}$ in characteristic $p(T)$.Comment: This article supersedes arXiv:1110.607

Preliminary observations on the use of a frame trawl in hydroacoustic surveys

Thirteen hauls were made during the hydroacoustic survey of the Ugandan waters of Lake Victoria from 7-19 February 1999. Ten of the hauls were made above the oxycline which was clearly visible as a strong echo on the echogram at between 25 and 35 m depth in most of the sampled areas. The remaining three hauls targeted the oxycline. Approximate equal weights of Rastrineobola argentia and Haplocromine cichlids were caught in total, but with marked differences between hauls. Near the surface R. argentia dominated the catches. In midwater Haplochromines were dominant. At the oxycline Caridina niloticus was abundan

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).

A complete characterization of Galois subfields of the generalized Giulietti--Korchm\'aros function field

We give a complete characterization of all Galois subfields of the generalized Giulietti--Korchm\'aros function fields \mathcal C_n / \fqn for $n\ge 5$. Calculating the genera of the corresponding fixed fields, we find new additions to the list of known genera of maximal function fields

Good families of Drinfeld modular curves

In this paper we investigate examples of good and optimal Drinfeld modular towers of function fields. Surprisingly, the optimality of these towers has not been investigated in full detail in the literature. We also give an algorithmic approach on how to obtain explicit defining equations for some of these towers and in particular give a new explicit example of an optimal tower over a quadratic finite field

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