Explicit Towers of Drinfeld Modular Curves

By Noam D. Elkies. 2000

73 citations recorded by the source corpus.

We give explicit equations for the simplest towers of Drinfeld modular curves over any finite field, and observe that they coincide with the asymptotically optimal towers of curves constructed by Garcia and Stichtenoth.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d6dc4bf2cc302ac540bef24e740318e8643f2a53

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Daniel Panario
2. Gary L. Mullen
3. Henning Stichtenoth
4. Arnaldo Garcia
5. Juscelino Bezerra

In Computational Theory and Mathematics

1. Daniel Panario
2. Gary L. Mullen
3. Henning Stichtenoth
4. Arnaldo Garcia

In Geometry and Topology

1. Henning Stichtenoth
2. Arnaldo Garcia
3. Daniel Panario
4. Gary L. Mullen

Citations in the corpus

• Towers of Function Fields over Non-prime Finite Fields (2012, background): “In the particular case of n = 2 and k = 1, these are just normalized Drinfeld modules together with T -isogenies (together with a T -torsion point in their kernel) as studied by Elkies in [4].”
• An explicit tower of function fields over cubic finite fields and Zink’s lower bound (2005, background): “Garcia and Stichtenoth [6] (see also [5]) gave an explicit and more elementary construction of such a sequence by introducing a tower of function fields F1 LF2 LF3 L over Fq2 as follows: Let F1 1⁄4 Fq2ðx1Þ be the rational function field, and for all if 1 let Fiþ1 1⁄4 Fiðxiþ1Þ with”
• Handbook of Finite Fields (2013, methodology): “3 Remark (Modular towers) [3, 7, 8, 27, 43] Modular towers were introduced by Ihara, and independently by Tsfasman, Vlăduţ and Zink.”