Explicit modular towers
<|reference_start|>Explicit modular towers: We give a general recipe for explicitly constructing asymptotically optimal towers of modular curves such as {X_0(l^n): n=1,2,3,...}. 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.<|reference_end|>
@article{elkies2001explicit,
    title={Explicit modular towers},
    author={Noam D. Elkies},
    journal={Pages 23-32 in Proceedings of the Thirty-Fifth Annual Allerton
  Conference on Communication, Control and Computing (1997; T.Basar and
  A.Vardy, eds.), Univ. of Illinois at Urbana-Champaign 1998},
    year={2001},
    archivePrefix={arXiv},
    eprint={math/0103107},
    primaryClass={math.NT cs.IT math.AG math.IT}
}