Algebraic Function Fields over ℤ3 by Niederreiter/Xing
Detailed examples for global function fields F/ℤ3 can be found in [1] for g(F/ℤ3) ≤ 15 and in [2] for g(F/ℤ3) ≥ 17.
In [2, Example 8B] it is shown that the function field with genus g = 25 and N = 36 rational places has also at least 6 places of degree 2. Similarly it is shown in [2, Example 12] that the function field with genus g = 29 and N = 42 rational places has at least 14 places of degree 5.
References
| [1] | Harald Niederreiter and Chaoping Xing. Cyclotomic function fields, Hilbert class fields, and global function fields with many rational places. Acta Arithmetica, 79(1):59–76, 1997. MR1438117 (97m:11141) |
| [2] | Harald Niederreiter and Chaoping Xing. Global function fields with many rational places over the ternary field. Acta Arithmetica, 83(1):65–86, 1998. MR1489567 (98j:11110) |
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. “Algebraic Function Fields over ℤ3 by Niederreiter/Xing.”
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