We give an explicit construction of an integral basis for a radical function field , where , under the assumptions and . The field discriminant of is also computed. We explain why these questions are substantially easier than the corresponding ones in number fields. Some formulae for the -signatures of a radical function field are also discussed in this paper.
Nous donnons une construction explicite d’une base entière pour le corps de fonction , où , sous l’hypothèse et . Le discriminant du corps est également calculé. Nous expliquons pourquoi ces questions sont considérablement plus faciles que dans le cas des corps de nombres. Quelques formules pour les -signatures des corps de fonction radiciels sont également présentées dans ce papier.
@article{JTNB_2010__22_1_259_0, author = {Qingquan Wu}, title = {Explicit construction of integral bases of radical function fields}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {259--270}, publisher = {Universit\'e Bordeaux 1}, volume = {22}, number = {1}, year = {2010}, doi = {10.5802/jtnb.714}, mrnumber = {2675883}, zbl = {1236.11089}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.714/} }
TY - JOUR AU - Qingquan Wu TI - Explicit construction of integral bases of radical function fields JO - Journal de théorie des nombres de Bordeaux PY - 2010 SP - 259 EP - 270 VL - 22 IS - 1 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.714/ DO - 10.5802/jtnb.714 LA - en ID - JTNB_2010__22_1_259_0 ER -
%0 Journal Article %A Qingquan Wu %T Explicit construction of integral bases of radical function fields %J Journal de théorie des nombres de Bordeaux %D 2010 %P 259-270 %V 22 %N 1 %I Université Bordeaux 1 %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.714/ %R 10.5802/jtnb.714 %G en %F JTNB_2010__22_1_259_0
Qingquan Wu. Explicit construction of integral bases of radical function fields. Journal de théorie des nombres de Bordeaux, Volume 22 (2010) no. 1, pp. 259-270. doi : 10.5802/jtnb.714. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.714/
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