# Explicit Modular Towers

 Title: Explicit Modular Towers Author: Elkies, Noam Citation: Elkies, 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. Full Text & Related Files: Elkies - Explicit modular towers.pdf (125.4Kb; PDF) Abstract: We 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. Published Version: Other Sources: http://www.math.harvard.edu/~elkies/math_pubs.html http://arxiv.org/abs/math/0103107 Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:2963974

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