Elkies, Noam2009-05-211997Elkies, Noam D. 1997. Explicit modular towers. In Proceedings of the Thirty-fifth annual Allerton conference on communication, control and computing. ed. Basar, Tamer, and Alexander Vardy, 23-32. Univ. of Illinois at Urbana-Champaign 1998.http://nrs.harvard.edu/urn-3:HUL.InstRepos:2963974We give a general recipe for explicitly constructing asymptotically optimal towers of modular curves such as \(\{X_0(l^n)\}_{n>1}\). We illustrate the method by giving equations for eight towers with various geometric features. We conclude by observing that such towers are all of a specific recursive form, and speculate that perhaps every tower of this form that attains the Drinfeld-Vladut bound is modular.en-US