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Good families of Drinfeld modular curves

Part of: Computational aspects in algebraic geometry Algebraic number theory: global fields Arithmetic algebraic geometry Curves

Published online by Cambridge University Press:  01 December 2015

Alp Bassa ,
Peter Beelen  and
Nhut Nguyen
Alp Bassa
Affiliation:
Boğaziçi University, Faculty of Arts and Sciences, Department of Mathematics, 34342 Bebek, İstanbul, Turkey email alp.bassa@boun.edu.tr
Peter Beelen
Affiliation:
Technical University of Denmark, Department of Applied Mathematics and Computer Science, Matematiktorvet 303B, 2800 Kgs. Lyngby, Denmark email pabe@dtu.dk
Nhut Nguyen
Affiliation:
Technical University of Denmark, Department of Applied Mathematics and Computer Science, Matematiktorvet 303B, 2800 Kgs. Lyngby, Denmark email nhngu@dtu.dk

Abstract

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In this paper, we investigate examples of good and optimal Drinfeld modular towers of function fields. Surprisingly, the optimality of these towers has not been investigated in full detail in the literature. We also give an algorithmic approach for obtaining explicit defining equations for some of these towers and, in particular, give a new explicit example of an optimal tower over a quadratic finite field.

MSC classification

Primary: 11G09: Drinfel'd modules; higher-dimensional motives, etc. 14H05: Algebraic functions; function fields 14H10: Families, moduli (algebraic)
Secondary: 11R58: Arithmetic theory of algebraic function fields 14Q05: Curves
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 18 , Issue 1 , 2015 , pp. 699 - 712
Copyright
© The Author(s) 2015 

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