## Drinfeld Modules of Rank 1

Using narrow ray class extensions obtained from Drinfelʹd modules of rank 1, new algebraic function fields can be constructed. These methods are developed in [1], yielding new fields over ℤ_{2} (and some over ℤ_{3}). In [2], similar methods are used for obtaining new fields over **F**_{4} (and one example over **F**_{8}). In [3], [2, Theorem 3] is used for constructing fields over **F**_{9} and **F**_{27}. The methods presented in [4] lead to fields over **F**_{4}, **F**_{8}, **F**_{9}, **F**_{16}, and **F**_{27}.

### See also

[5, Section 4.2]

### References

[1] | Chaoping Xing and Harald Niederreiter. Drinfeld modules of rank 1 and algebraic curves with many rational points. Monatshefte für Mathematik, 127(3):219–241, April 1999.doi:10.1007/s006050050036 MR1680515 (2000a:11088) |

[2] | Harald Niederreiter and Chaoping Xing. Drinfeld modules of rank 1 and algebraic curves with many rational points. II. Acta Arithmetica, 81(1):81–100, 1997.MR1454158 (99d:11064) |

[3] | Harald Niederreiter and Chaoping Xing. Nets, ( t, s)-sequences, and algebraic geometry.In Peter Hellekalek and Gerhard Larcher, editors, Random and Quasi-Random Point Sets, volume 138 of Lecture Notes in Statistics, pages 267–302. Springer-Verlag, 1998. |

[4] | Harald Niederreiter and Chaoping Xing. A general method of constructing global function fields with many rational places. In J. P. Buhler, editor, Algorithmic Number Theory, volume 1423 of Lecture Notes in Computer Science, pages 555–566. Springer-Verlag, 1998.doi:10.1007/BFb0054892 |

[5] | Harald Niederreiter and Chaoping Xing.Rational Points on Curves over Finite Fields: Theory and Applications, volume 285 of Lect. Note Series of the London Math. Soc.Cambridge University Press, 2001. MR1837382 (2002h:11055) |

### Copyright

Copyright © 2004, 2005, 2006, 2007, 2008, 2009, 2010 by Rudolf Schürer and Wolfgang Ch. Schmid.

Cite this as: Rudolf Schürer and Wolfgang Ch. Schmid. “Drinfeld Modules of Rank 1.”
From MinT—the database of optimal net, code, OA, and OOA parameters.
Version: 2008-04-04.
http://mint.sbg.ac.at/desc_FDrinfeld.html