Explicit modular towers

Details Explicit modular towers Explicit modular towers

2001-03-16

arxiv.org/abs/math/0103107v1

Pages 23-32 in Proceedings of the Thirty-Fifth Annual Allerton Conference on Communication, Control and Computing (1997; T.Bas

Mathematics

Number Theory

10 pages; presented at Allerton 1998 (see Journal-ref field)

Scientific paper

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.

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