Publication: Explicit Modular Towers
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1997
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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.
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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.
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